Solve For { X $} : : : { -12x - 17 = -89 \}

Mar 10, 2025 by ADMIN 44 views

Solve for $x$: $-12x - 17 = -89$

Introduction

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. In this article, we will focus on solving a linear equation with one variable, $x$ . The given equation is $-12x - 17 = -89$ , and our goal is to find the value of $x$ that satisfies this equation.

Understanding the Equation

The given equation is a linear equation in the form of $ax + b = c$ , where $a$ , $b$ , and $c$ are constants. In this case, $a = -12$ , $b = -17$ , and $c = -89$ . Our objective is to isolate the variable $x$ by performing algebraic operations on both sides of the equation.

Step 1: Add 17 to Both Sides

To start solving the equation, we need to get rid of the constant term on the left-hand side. We can do this by adding 17 to both sides of the equation. This will result in:

-12x - 17 + 17 = -89 + 17

Simplifying the equation, we get:

-12x = -72

Step 2: Divide Both Sides by -12

Now that we have isolated the term with the variable, we need to get rid of the coefficient of $x$ . In this case, the coefficient is $-12$ . We can do this by dividing both sides of the equation by $-12$ . This will result in:

\frac{-12x}{-12} = \frac{-72}{-12}

Simplifying the equation, we get:

x = 6

Conclusion

In this article, we solved a linear equation with one variable, $x$ . The given equation was $-12x - 17 = -89$ , and our goal was to find the value of $x$ that satisfies this equation. By following the steps outlined above, we were able to isolate the variable $x$ and find its value.

Tips and Tricks

When solving linear equations, it is essential to follow the order of operations (PEMDAS) to ensure that the equation is simplified correctly.
When adding or subtracting constants to both sides of the equation, make sure to keep the equation balanced by performing the same operation on both sides.
When dividing both sides of the equation by a coefficient, make sure to simplify the equation correctly by canceling out the coefficient.

Real-World Applications

Solving linear equations has numerous real-world applications in various fields, including:

Physics: Solving linear equations is essential in physics to describe the motion of objects and to calculate forces and energies.
Engineering: Linear equations are used in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Linear equations are used in economics to model the behavior of economic systems and to make predictions about future trends.

Common Mistakes

When solving linear equations, it is essential to avoid common mistakes, such as:

Not following the order of operations (PEMDAS)
Not keeping the equation balanced by performing the same operation on both sides
Not simplifying the equation correctly by canceling out coefficients

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. By following the steps outlined above, we can solve linear equations with one variable and find the value of the variable that satisfies the equation.

Introduction

In our previous article, we solved a linear equation with one variable, $x$ . The given equation was $-12x - 17 = -89$ , and our goal was to find the value of $x$ that satisfies this equation. In this article, we will answer some frequently asked questions (FAQs) related to solving linear equations.

Q&A

Q: What is the first step in solving a linear equation?

A: The first step in solving a linear equation is to simplify the equation by combining like terms. This involves adding or subtracting constants to both sides of the equation to isolate the term with the variable.

Q: How do I know which operation to perform on both sides of the equation?

A: To determine which operation to perform on both sides of the equation, you need to identify the coefficient of the variable. If the coefficient is positive, you can add or subtract constants to both sides of the equation. If the coefficient is negative, you need to multiply or divide both sides of the equation by a negative number.

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. For example, $2x + 3 = 5$ is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I solve a linear equation with a fraction as a coefficient?

A: To solve a linear equation with a fraction as a coefficient, you need to multiply or divide both sides of the equation by the denominator of the fraction. This will eliminate the fraction and allow you to solve the equation.

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 simplifying an expression. The acronym PEMDAS stands for:

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

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you need to plug the value of the variable back into the original equation and simplify. If the equation is true, then your solution is correct.