Question
Solve for x in simplest form. \[ 9=\frac{1}{3}(4 x-12) \]
Ask by Goodwin Adkins. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = \frac{39}{4} \) or \( x = 9.75 \)
Solution
Solve the equation \( 9=\frac{1}{3}(4x-12) \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(9=\frac{1}{3}\left(4x-12\right)\)
- step1: Multiply the terms:
\(9=\frac{4}{3}x-4\)
- step2: Swap the sides:
\(\frac{4}{3}x-4=9\)
- step3: Move the constant to the right side:
\(\frac{4}{3}x=9+4\)
- step4: Add the numbers:
\(\frac{4}{3}x=13\)
- step5: Multiply by the reciprocal:
\(\frac{4}{3}x\times \frac{3}{4}=13\times \frac{3}{4}\)
- step6: Multiply:
\(x=\frac{39}{4}\)
The solution to the equation \(9=\frac{1}{3}(4x-12)\) in simplest form is \(x=\frac{39}{4}\) or \(x=9.75\).
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Beyond the Answer
First, let's tackle that equation step-by-step. To eliminate the fraction, multiply both sides by 3: \[ 3 \times 9 = 4x - 12 \] This simplifies down to: \[ 27 = 4x - 12 \] Now, we want to isolate \( 4x \). Add 12 to both sides: \[ 27 + 12 = 4x \] So, we get: \[ 39 = 4x \] Now, divide both sides by 4 to solve for \( x \): \[ x = \frac{39}{4} \] Thus, the simplest form of \( x \) is: \[ x = 9.75 \text{ or } x = \frac{39}{4} \] depending on how you prefer to express it!
