Question
Which value of \( v \) makes \( 12=12+\frac{v-8}{2} \) a true statement?
Ask by Sandoval Hart. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( v=8 \)
Solution
Solve the equation \( 12=12+\frac{v-8}{2} \).
Solve the equation by following steps:
- step0: Solve for \(v\):
\(12=12+\frac{v-8}{2}\)
- step1: Swap the sides:
\(12+\frac{v-8}{2}=12\)
- step2: Multiply both sides of the equation by LCD:
\(\left(12+\frac{v-8}{2}\right)\times 2=12\times 2\)
- step3: Simplify the equation:
\(16+v=24\)
- step4: Move the constant to the right side:
\(v=24-16\)
- step5: Subtract the numbers:
\(v=8\)
The value of \( v \) that makes the statement \( 12=12+\frac{v-8}{2} \) true is \( v=8 \).
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Simplify this solution The Deep Dive
To solve the equation \( 12 = 12 + \frac{v - 8}{2} \), we can start by simplifying it. First, we can subtract 12 from both sides: \[ 12 - 12 = \frac{v - 8}{2} \] This simplifies to: \[ 0 = \frac{v - 8}{2} \] Next, we multiply both sides by 2 to eliminate the fraction: \[ 0 \cdot 2 = v - 8 \] This simplifies to: \[ 0 = v - 8 \] Now, by adding 8 to both sides, we find: \[ v = 8 \] So, the value of \( v \) that makes the equation true is \( \boxed{8} \).
