Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -\frac{5}{3} \)
Solution
To solve the equation:
\[
8(4x + 8) = 11 - (x + 2)
\]
**Step 1: Expand both sides**
First, distribute the multiplication on the left side and simplify the right side:
\[
8 \times 4x + 8 \times 8 = 11 - x - 2
\]
\[
32x + 64 = 9 - x
\]
**Step 2: Move all \(x\) terms to one side and constant terms to the other**
Add \(x\) to both sides to get all \(x\) terms on the left:
\[
32x + x + 64 = 9
\]
\[
33x + 64 = 9
\]
Subtract 64 from both sides to isolate the \(x\) term:
\[
33x = 9 - 64
\]
\[
33x = -55
\]
**Step 3: Solve for \(x\)**
Divide both sides by 33:
\[
x = \frac{-55}{33}
\]
Simplify the fraction by dividing numerator and denominator by 11:
\[
x = \frac{-5}{3}
\]
**Final Answer:**
\[
x = -\frac{5}{3}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the equation \( 8(4x + 8) = 11 - (x + 2) \), we start by simplifying both sides. First, distribute on the left: \( 32x + 64 = 11 - x - 2 \). Now, simplify the right side: \( 32x + 64 = 9 - x \). Next, let's add \( x \) to both sides: \( 32x + x + 64 = 9 \) \( 33x + 64 = 9 \). Now, subtract 64 from both sides: \( 33x = 9 - 64 \) \( 33x = -55 \). Finally, divide both sides by 33: \( x = -\frac{55}{33} \) \( x = -\frac{5}{3} \). So the solution to the equation is \( x = -\frac{5}{3} \).
