Select The Correct Answer.Which Value Of $x$ Makes This Equation True?$-5(x-20)=35$A. 27 B. -3 C. 13 D. -11

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific linear equation, $-5(x-20)=35$, and determine the value of $x$ that makes this equation true.

Understanding the Equation

The given equation is a linear equation in one variable, $x$. It involves a coefficient of $-5$, which is multiplied by the expression $(x-20)$. The equation is set equal to $35$, indicating that the solution will be a value of $x$ that satisfies this equation.

Step 1: Distribute the Coefficient

To solve the equation, we need to start by distributing the coefficient $-5$ to the terms inside the parentheses. This will give us:

$$-5x + 100 = 35$$

Step 2: Isolate the Variable

Next, we need to isolate the variable $x$ by getting rid of the constant term on the left-hand side of the equation. We can do this by subtracting $100$ from both sides of the equation:

$$-5x = -65$$

Step 3: Solve for x

Now that we have isolated the variable, we can solve for $x$ by dividing both sides of the equation by $-5$:

$$x = \frac{-65}{-5}$$

Simplifying the Expression

To simplify the expression, we can divide the numerator and denominator by their greatest common divisor, which is $5$:

$$x = \frac{-13}{1}$$

Conclusion

Therefore, the value of $x$ that makes the equation $-5(x-20)=35$ true is $x = -13$.

Answer

The correct answer is:

• D. -11 is incorrect
• A. 27 is incorrect
• B. -3 is incorrect
• C. 13 is incorrect
• D. -11 is incorrect
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  Solving Linear Equations: A Q&A Guide =====================================

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations in solving linear equations?

A: The order of operations in solving linear equations is:

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I handle negative coefficients in linear equations?

A: When working with negative coefficients in linear equations, you need to remember that a negative coefficient changes the direction of the inequality. For example, if you have the equation $-2x = 6$, you would divide both sides by $-2$ to get $x = -3$.

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

Q: Can I use algebraic methods to solve linear equations?

A: Yes, you can use algebraic methods to solve linear equations. Some common algebraic methods include:

• Adding or subtracting the same value to both sides of the equation
• Multiplying or dividing both sides of the equation by the same value
• Using inverse operations to isolate the variable

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Not following the order of operations
• Not isolating the variable on one side of the equation
• Not checking the solution to make sure it satisfies the original equation

Q: Can I use technology to solve linear equations?

A: Yes, you can use technology to solve linear equations. Some common tools include:

• Graphing calculators
• Online equation solvers
• Computer algebra systems

Q: What are some real-world applications of linear equations?

A: Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

Solving linear equations is an essential skill in mathematics and has many real-world applications. By following the steps outlined in this article, you can learn how to solve linear equations and apply them to a variety of problems. Remember to always check your solution to make sure it satisfies the original equation, and don't be afraid to use technology to help you solve linear equations.