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Chapter 2: Problem 32

Solve each linear equation. Show your work and check your answer. $$14=-5 x-21$$

Short Answer

Expert verified
x = -7

Step by step solution

01

Add 21 to both sides

To isolate the variable term \(-5x\), first add 21 to both sides of the equation:\[ 14 + 21 = -5x - 21 + 21 \]This simplifies to:\[ 35 = -5x \]
02

Divide by -5

To solve for \(x\), divide both sides of the equation by \(-5\):\[ \frac{35}{-5} = \frac{-5x}{-5} \]This simplifies to:\[ -7 = x \]
03

Check the solution

Substitute \(x = -7\) back into the original equation to check the solution:\[ 14 = -5(-7) - 21 \]Calculate the right-hand side:\[ -5(-7) = 35 \]So:\[ 35 - 21 = 14 \]Since both sides of the equation are equal, \(x = -7\) is the correct solution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables
Isolating the variable is the key to solving linear equations. Here's how to do it step by step:
  • First, identify the variable you need to solve for. In our example, it's \( x \).
  • Start with the original equation: \( 14 = -5x - 21 \).
  • Your goal is to get \( x \) by itself on one side of the equation. To start this process, we need to remove the constant (\

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