Question
What value of \( a \) is a solution to this equation? \( -2 a+8(a-4)=-74 \) \( a=-7 \) \( a=9 \)
Ask by Rogers Vaughn. in the United States
Jan 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( a=-7 \)
Solution
Solve the equation \( -2a+8(a-4)=-74 \).
Solve the equation by following steps:
- step0: Solve for \(a\):
\(-2a+8\left(a-4\right)=-74\)
- step1: Move the expression to the left side:
\(-2a+8\left(a-4\right)-\left(-74\right)=0\)
- step2: Remove the parentheses:
\(-2a+8\left(a-4\right)+74=0\)
- step3: Calculate:
\(6a+42=0\)
- step4: Move the constant to the right side:
\(6a=0-42\)
- step5: Remove 0:
\(6a=-42\)
- step6: Divide both sides:
\(\frac{6a}{6}=\frac{-42}{6}\)
- step7: Divide the numbers:
\(a=-7\)
The solution to the equation \( -2a+8(a-4)=-74 \) is \( a=-7 \).
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Simplify this solution Mind Expander
To solve the equation \( -2 a + 8(a - 4) = -74 \), let's simplify it step by step. First, distribute the 8: \[ -2a + 8a - 32 = -74 \] Now, combine like terms: \[ 6a - 32 = -74 \] Next, add 32 to both sides to isolate the term with \( a \): \[ 6a = -74 + 32 \] This simplifies to: \[ 6a = -42 \] Now, divide both sides by 6 to solve for \( a \): \[ a = -7 \] Therefore, the value of \( a \) is \( -7 \). Double-checking the options presented, we find \( a = -7 \) fits the solution perfectly!
