Question $-4(3 x+2)=16$

Studdy Solution

STEP 1

1. The equation $-4(3x + 2) = 16$ is a linear equation.
2. The goal is to solve for the variable $x$ .
3. The equation involves distribution and basic algebraic operations.

STEP 2

1. Distribute the multiplication over addition inside the parentheses.
2. Simplify the equation to isolate the term containing $x$ .
3. Solve for $x$ by performing algebraic operations.
4. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the $-4$ across the terms inside the parentheses:
$-4 \times 3x + (-4) \times 2 = 16$
This simplifies to:
$-12x - 8 = 16$

STEP 4

Add $8$ to both sides of the equation to isolate the term with $x$ :
$-12x - 8 + 8 = 16 + 8$
This simplifies to:
$-12x = 24$

STEP 5

Divide both sides by $-12$ to solve for $x$ :
$\frac{-12x}{-12} = \frac{24}{-12}$
This simplifies to:
$x = -2$

STEP 6

Check the solution by substituting $x = -2$ back into the original equation:
$-4(3(-2) + 2) = 16$
Simplify inside the parentheses:
$-4(-6 + 2) = 16$
$-4(-4) = 16$
$16 = 16$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{-2}$

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