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Chapter 1: Problem 15

Solve each equation and check your answer. $$-3 x+6=12$$

Short Answer

Expert verified
x = -2

Step by step solution

01

Isolate the variable term

First, move the constant term to the other side of the equation by subtracting 6 from both sides. \[ -3x + 6 - 6 = 12 - 6 \] This simplifies to: \[ -3x = 6 \]
02

Solve for the variable

Next, divide both sides of the equation by -3 to isolate x. \[ \frac{-3x}{-3} = \frac{6}{-3} \] This simplifies to: \[ x = -2 \]
03

Check the solution

To verify the solution, substitute x back into the original equation. \[ -3(-2) + 6 = 12 \] This simplifies to: \[ 6 + 6 = 12 \] Thus, the left-hand side equals the right-hand side, confirming that the solution is correct.

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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 a crucial step in solving linear equations. It means getting the variable (like x) by itself on one side of the equation.
To start, identify the operations around the variable. In our example, \( -3x + 6 = 12 \), the variable term is \(-3x\).
To isolate x, first we need to move the constant term, 6.
We do that by subtracting 6 from both sides:
\[ -3x + 6 - 6 = 12 - 6 \]
Simplifying both sides, we get:
\[ -3x = 6 \]
  • Move constant terms using addition or subtraction
  • Always perform the same operation on both sides of the equation
Now x is closer to being isolated!
checking solutions
Verifying your solution is an important step to ensure accuracy.
After finding x, substitute it back into the original equation and check if both sides equal.
From our example:
Our solution for x is -2. Substitute x into the equation:
\[ -3(-2) + 6 \]
This simplifies to:
\[ 6 + 6 \]
  • If both sides match, the solution is correct
  • If they don鈥檛 match, recheck your steps
Simplifying further, we see:
\

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