Boone Lane
03/03/2024 · Middle School
\( 6(x-6)+2=8(x+2)-8 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is \( x=\square \). (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.
UpStudy ThothAI Solution
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Step-by-step Solution
Solve the equation \( 6(x-6)+2=8(x+2)-8 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(6\left(x-6\right)+2=8\left(x+2\right)-8\)
- step1: Move the expression to the left side:
\(6\left(x-6\right)+2-\left(8\left(x+2\right)-8\right)=0\)
- step2: Calculate:
\(6\left(x-6\right)+10-8\left(x+2\right)=0\)
- step3: Calculate:
\(-2x-42=0\)
- step4: Move the constant to the right side:
\(-2x=0+42\)
- step5: Remove 0:
\(-2x=42\)
- step6: Change the signs:
\(2x=-42\)
- step7: Divide both sides:
\(\frac{2x}{2}=\frac{-42}{2}\)
- step8: Divide the numbers:
\(x=-21\)
The solution to the equation \(6(x-6)+2=8(x+2)-8\) is \(x=-21\).
Therefore, the correct choice is:
A. The solution is \(x=-21\).
Quick Answer
The solution is \(x=-21\).
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