Solving Linear Equations: A Step-by-Step Guide

Solving for the variable 'x' in linear equations is a fundamental skill in high school mathematics. In this article, we'll dive into the process of solving the equation '5(x - 6) - 7(x + 2) = -16' and provide a detailed explanation to help you master this concept.

Step 1: Distribute the Coefficients

The first step in solving this equation is to distribute the coefficients to both sides of the equation. This means we need to multiply the terms inside the parentheses by their respective coefficients.

On the left side of the equation, we have:

• 5(x - 6) = 5x - 30
• -7(x + 2) = -7x - 14

Now, we can combine these terms:

• 5x - 30 - 7x - 14 = -16

Step 2: Combine Like Terms

The next step is to combine the like terms on the left side of the equation. In this case, the like terms are the 'x' terms and the constant terms.

• 5x - 7x = -2x
• -30 - 14 = -44

Now, the equation becomes:

• -2x - 44 = -16

Step 3: Isolate the Variable

To solve for the variable 'x', we need to isolate it on one side of the equation. We can do this by adding 44 to both sides of the equation.

• -2x - 44 + 44 = -16 + 44
• -2x = 28

Step 4: Divide to Find the Value of x

The final step is to divide both sides of the equation by -2 to find the value of 'x'.

• -2x / -2 = 28 / -2
• x = -14

Therefore, the solution to the equation '5(x - 6) - 7(x + 2) = -16' is x = -14.

By following these steps, you can solve any linear equation and find the value of the variable 'x'. Remember to carefully distribute the coefficients, combine like terms, isolate the variable, and divide to find the final solution.