Question
Go Solve each equation for the indicated variab 6. \( \quad 3(x-2)=5 x+8 ; \quad \) Solve for \( x \)
Ask by Rowe Kelley. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = -7 \)
Solution
To solve the equation 3(x - 2) = 5x + 8 for x, follow these steps:
1. Distribute the 3 on the left side:
3x - 6 = 5x + 8
2. Subtract 3x from both sides to gather the x terms on the right:
-6 = 2x + 8
3. Subtract 8 from both sides to isolate the term with x:
-14 = 2x
4. Divide both sides by 2:
x = -7
Thus, the solution for x is -7.
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Simplify this solution Beyond the Answer
First, let's distribute the \( 3 \) on the left side of the equation: \( 3(x - 2) = 3x - 6 \). So we have the equation \( 3x - 6 = 5x + 8 \). Next, let's move all the \( x \) terms to one side by subtracting \( 3x \) from both sides: \( -6 = 2x + 8 \). Now, subtract \( 8 \) from both sides to isolate the \( x \) term: \( -6 - 8 = 2x \), which simplifies to \( -14 = 2x \). Finally, divide both sides by \( 2 \): \( x = -7 \). The solution for \( x \) is \( -7 \).
