What Is The Value Of $x$ In The Equation $-\frac{3}{4}=\frac{x}{24}$?A. -32 B. -18 C. 18 D. 32

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving a simple equation involving fractions. The equation $-\frac{3}{4}=\frac{x}{24}$ requires us to isolate the variable $x$ and find its value. We will use basic algebraic operations to solve this equation and provide the correct answer.

Understanding the Equation

The given equation is $-\frac{3}{4}=\frac{x}{24}$. To solve for $x$, we need to isolate the variable on one side of the equation. The equation involves fractions, so we will use the concept of equivalent ratios to simplify it.

Step 1: Multiply Both Sides by 24

To eliminate the fraction on the right-hand side, we can multiply both sides of the equation by 24. This will help us get rid of the fraction and make it easier to solve for $x$.

$$-\frac{3}{4}=\frac{x}{24}$$

$$\implies -\frac{3}{4} \times 24 = \frac{x}{24} \times 24$$

$$\implies -18 = x$$

Step 2: Simplify the Equation

By multiplying both sides of the equation by 24, we have simplified the equation and isolated the variable $x$. The equation now becomes $-18 = x$.

Conclusion

In this article, we have solved the equation $-\frac{3}{4}=\frac{x}{24}$ and found the value of $x$. By multiplying both sides of the equation by 24, we have isolated the variable $x$ and simplified the equation. The correct answer is $-18$.

Final Answer

The final answer to the equation $-\frac{3}{4}=\frac{x}{24}$ is $\boxed{-18}$.

Why is this the Correct Answer?

The correct answer is $-18$ because when we multiply both sides of the equation by 24, we get $-18 = x$. This means that the value of $x$ is $-18$.

What is the Importance of Solving Equations?

Solving equations is an essential concept in mathematics that helps us find the value of unknown variables. It is used in various fields such as science, engineering, and economics to solve real-world problems. By solving equations, we can understand the relationships between variables and make informed decisions.

How to Solve Equations?

To solve equations, we need to follow the order of operations (PEMDAS) and use basic algebraic operations such as addition, subtraction, multiplication, and division. We can also use inverse operations to isolate the variable and solve for its value.

What are the Different Types of Equations?

There are different types of equations such as linear equations, quadratic equations, and polynomial equations. Each type of equation has its own set of rules and operations that we need to follow to solve it.

What is the Difference Between an Equation and an Expression?

An equation is a statement that says two expressions are equal, while an expression is a group of numbers and variables combined using mathematical operations. For example, $x + 3$ is an expression, while $x + 3 = 5$ is an equation.

What is the Importance of Understanding Fractions?

Understanding fractions is essential in mathematics because it helps us solve equations involving fractions. Fractions are used to represent parts of a whole, and they are used in various mathematical operations such as addition, subtraction, multiplication, and division.

How to Simplify Fractions?

To simplify fractions, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. For example, to simplify the fraction $\frac{12}{16}$, we need to find the GCD of 12 and 16, which is 4. Then, we divide both numbers by 4 to get $\frac{3}{4}$.

What is the Difference Between a Fraction and a Decimal?

A fraction is a way of representing a part of a whole, while a decimal is a way of representing a fraction as a decimal number. For example, the fraction $\frac{1}{2}$ is equal to the decimal 0.5.

What is the Importance of Understanding Ratios?

Understanding ratios is essential in mathematics because it helps us solve equations involving ratios. Ratios are used to compare two or more quantities, and they are used in various mathematical operations such as addition, subtraction, multiplication, and division.

How to Simplify Ratios?

To simplify ratios, we need to find the greatest common divisor (GCD) of the two numbers and divide both numbers by the GCD. For example, to simplify the ratio $\frac{12}{16}$, we need to find the GCD of 12 and 16, which is 4. Then, we divide both numbers by 4 to get $\frac{3}{4}$.

What is the Difference Between a Ratio and a Proportion?

A ratio is a way of comparing two or more quantities, while a proportion is a statement that says two ratios are equal. For example, the ratio $\frac{1}{2}$ is equal to the proportion $\frac{1}{2} = \frac{3}{6}$.

What is the Importance of Understanding Proportions?

Understanding proportions is essential in mathematics because it helps us solve equations involving proportions. Proportions are used to compare two or more ratios, and they are used in various mathematical operations such as addition, subtraction, multiplication, and division.

How to Solve Proportions?

To solve proportions, we need to follow the order of operations (PEMDAS) and use basic algebraic operations such as addition, subtraction, multiplication, and division. We can also use inverse operations to isolate the variable and solve for its value.

What is the Difference Between a Proportion and an Equation?

A proportion is a statement that says two ratios are equal, while an equation is a statement that says two expressions are equal. For example, the proportion $\frac{1}{2} = \frac{3}{6}$ is equal to the equation $x + 3 = 5$.

What is the Importance of Understanding Algebraic Operations?

Understanding algebraic operations is essential in mathematics because it helps us solve equations involving variables. Algebraic operations such as addition, subtraction, multiplication, and division are used to manipulate variables and solve equations.

How to Use Algebraic Operations to Solve Equations?

To use algebraic operations to solve equations, we need to follow the order of operations (PEMDAS) and use basic algebraic operations such as addition, subtraction, multiplication, and division. We can also use inverse operations to isolate the variable and solve for its value.

What is the Difference Between an Algebraic Operation and a Mathematical Operation?

An algebraic operation is a mathematical operation that involves variables, while a mathematical operation is a mathematical operation that involves numbers. For example, the algebraic operation $x + 3$ is equal to the mathematical operation $5 + 3$.

What is the Importance of Understanding Inverse Operations?

Understanding inverse operations is essential in mathematics because it helps us solve equations involving variables. Inverse operations such as addition and subtraction, multiplication and division, and exponentiation and logarithm are used to isolate the variable and solve for its value.

How to Use Inverse Operations to Solve Equations?

To use inverse operations to solve equations, we need to follow the order of operations (PEMDAS) and use basic algebraic operations such as addition, subtraction, multiplication, and division. We can also use inverse operations to isolate the variable and solve for its value.

What is the Difference Between an Inverse Operation and a Mathematical Operation?

An inverse operation is a mathematical operation that involves variables, while a mathematical operation is a mathematical operation that involves numbers. For example, the inverse operation $x - 3$ is equal to the mathematical operation $5 - 3$.

What is the Importance of Understanding Exponentiation and Logarithm?

Understanding exponentiation and logarithm is essential in mathematics because it helps us solve equations involving variables. Exponentiation and logarithm are used to manipulate variables and solve equations.

How to Use Exponentiation and Logarithm to Solve Equations?

To use exponentiation and logarithm to solve equations, we need to follow the order of operations (PEMDAS) and use basic algebraic operations such as addition, subtraction, multiplication, and division. We can also use exponentiation and logarithm to isolate the variable and solve for its value.

What is the Difference Between Exponentiation and Logarithm?

Exponentiation is a mathematical operation that involves raising a number to a power, while logarithm is a mathematical operation that involves finding the power to which a number must be raised to produce a given value. For example, the exponentiation $2^3$ is equal to the logarithm $log_2(8)$.

What is the Importance of Understanding Mathematical Operations?

Understanding mathematical operations is essential in mathematics because it helps us solve equations involving variables. Mathematical operations such as addition, subtraction, multiplication, and division are used to manipulate variables and solve equations.

How to Use Mathematical Operations to Solve Equations?

To use mathematical operations to solve equations, we need to follow the order of operations (PEMDAS) and use basic algebraic operations such as addition, subtraction, multiplication, and division. We can also use mathematical operations to isolate the variable and solve for its value.

What is the Difference Between a Mathematical Operation and an Algebraic Operation?

A mathematical operation is a mathematical operation that involves numbers, while an algebraic operation is a mathematical operation that

Q: What is the first step in solving an equation?

A: The first step in solving an equation is to read and understand the equation. This involves identifying the variables, constants, and mathematical operations involved in the equation.

Q: How do I isolate the variable in an equation?

A: To isolate the variable in an equation, you need to use inverse operations to get the variable by itself on one side of the equation. This involves using operations such as addition, subtraction, multiplication, and division to eliminate the constants and other variables.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:

• P: Parentheses (evaluate expressions inside parentheses first)
• E: Exponents (evaluate any exponential expressions next)
• M: Multiplication and Division (perform multiplication and division operations from left to right)
• A: Addition and Subtraction (perform addition and subtraction operations from left to right)

Q: How do I use inverse operations to solve an equation?

A: To use inverse operations to solve an equation, you need to identify the operation that is being performed on the variable and then use the inverse operation to eliminate it. For example, if the equation is x + 3 = 5, you can use the inverse operation of subtraction to eliminate the 3 and get x = 2.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation x + 3 = 5 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. You can also use factoring or the quadratic formula to solve the equation.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that is used to solve quadratic equations. It is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation.

Q: How do I use the quadratic formula to solve an equation?

A: To use the quadratic formula to solve an equation, you need to identify the coefficients a, b, and c in the equation and then plug them into the formula. You can then simplify the expression and solve for x.

Q: What is the difference between a system of equations and a single equation?

A: A system of equations is a set of two or more equations that are solved together, while a single equation is a single equation that is solved on its own.

Q: How do I solve a system of equations?

A: To solve a system of equations, you can use substitution or elimination to find the values of the variables. You can also use graphing or matrices to solve the system.

Q: What is the difference between substitution and elimination?

A: Substitution is a method of solving a system of equations by substituting one equation into the other, while elimination is a method of solving a system of equations by adding or subtracting the equations to eliminate one of the variables.

Q: How do I use substitution to solve a system of equations?

A: To use substitution to solve a system of equations, you need to identify one of the equations and substitute it into the other equation. You can then solve for the variable and find the values of the other variables.

Q: How do I use elimination to solve a system of equations?

A: To use elimination to solve a system of equations, you need to identify one of the equations and add or subtract it from the other equation to eliminate one of the variables. You can then solve for the variable and find the values of the other variables.

Q: What is the difference between a linear inequality and a quadratic inequality?

A: A linear inequality is an inequality in which the highest power of the variable is 1, while a quadratic inequality is an inequality in which the highest power of the variable is 2.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you can use the following steps:

• Write the inequality in the form of an equation
• Solve the equation
• Check the solution by plugging it back into the inequality

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you can use the following steps:

• Write the inequality in the form of an equation
• Solve the equation
• Check the solution by plugging it back into the inequality
• Use the quadratic formula to find the solutions to the equation
• Plot the solutions on a number line
• Determine the intervals on the number line that satisfy the inequality

Q: What is the difference between a rational expression and a polynomial expression?

A: A rational expression is an expression that is the ratio of two polynomials, while a polynomial expression is an expression that is a sum of terms, each of which is a product of a variable and a constant.

Q: How do I simplify a rational expression?

A: To simplify a rational expression, you need to factor the numerator and denominator and then cancel out any common factors.

Q: What is the difference between a rational inequality and a polynomial inequality?

A: A rational inequality is an inequality that involves a rational expression, while a polynomial inequality is an inequality that involves a polynomial expression.

Q: How do I solve a rational inequality?

A: To solve a rational inequality, you need to follow the same steps as solving a rational expression, but with the added step of checking the solution by plugging it back into the inequality.

Q: How do I solve a polynomial inequality?

A: To solve a polynomial inequality, you need to follow the same steps as solving a polynomial expression, but with the added step of checking the solution by plugging it back into the inequality.

Q: What is the difference between a system of inequalities and a single inequality?

A: A system of inequalities is a set of two or more inequalities that are solved together, while a single inequality is a single inequality that is solved on its own.

Q: How do I solve a system of inequalities?

A: To solve a system of inequalities, you need to use the same methods as solving a system of equations, but with the added step of checking the solution by plugging it back into the inequalities.

Q: What is the difference between a linear programming problem and a quadratic programming problem?

A: A linear programming problem is a problem that involves maximizing or minimizing a linear function subject to a set of linear constraints, while a quadratic programming problem is a problem that involves maximizing or minimizing a quadratic function subject to a set of linear constraints.

Q: How do I solve a linear programming problem?

A: To solve a linear programming problem, you need to use the following steps:

• Write the problem in the form of a linear equation
• Solve the equation
• Check the solution by plugging it back into the equation

Q: How do I solve a quadratic programming problem?

A: To solve a quadratic programming problem, you need to use the following steps:

• Write the problem in the form of a quadratic equation
• Solve the equation
• Check the solution by plugging it back into the equation
• Use the quadratic formula to find the solutions to the equation
• Plot the solutions on a number line
• Determine the intervals on the number line that satisfy the inequality