Questions: Solve for (x). 8(x-2)=-32 x=[?]

Transcript text: Solve for $x$. \[ \begin{array}{c} 8(x-2)=-32 \\ x=[?] \end{array} \]

Solution

Solution Steps

To solve for $ x $ in the equation $ 8(x-2) = -32 $, we need to isolate $ x $. First, we will distribute the 8 on the left side, then add or subtract terms to isolate $ x $.

Step 1: Distribute the 8

First, distribute the 8 on the left side of the equation: \[ 8(x - 2) = -32 \implies 8x - 16 = -32 \]

Step 2: Isolate the $ x $-term

Next, add 16 to both sides of the equation to isolate the $ x $-term: \[ 8x - 16 + 16 = -32 + 16 \implies 8x = -16 \]

Step 3: Solve for $ x $

Finally, divide both sides by 8 to solve for $ x $: \[ x = \frac{-16}{8} \implies x = -2 \]

Final Answer

\[ \boxed{x = -2} \]

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