Question
Solve the following proportion for \( x \) : \[ \frac{x-1}{2}=\frac{x+2}{8} \] Select one: a. \( -1 / 4 \) b. 2 c. 6 d. -3
Ask by Donnelly Long. in the United States
Nov 13,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The correct answer is b. 2.
Solution
Solve the equation \( \frac{x-1}{2}=\frac{x+2}{8} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{x-1}{2}=\frac{x+2}{8}\)
- step1: Cross multiply:
\(\left(x-1\right)\times 8=2\left(x+2\right)\)
- step2: Simplify the equation:
\(8\left(x-1\right)=2\left(x+2\right)\)
- step3: Rewrite the expression:
\(2\times 4\left(x-1\right)=2\left(x+2\right)\)
- step4: Evaluate:
\(4\left(x-1\right)=x+2\)
- step5: Expand the expression:
\(4x-4=x+2\)
- step6: Move the variable to the left side:
\(4x-4-x=2\)
- step7: Subtract the terms:
\(3x-4=2\)
- step8: Move the constant to the right side:
\(3x=2+4\)
- step9: Add the numbers:
\(3x=6\)
- step10: Divide both sides:
\(\frac{3x}{3}=\frac{6}{3}\)
- step11: Divide the numbers:
\(x=2\)
The solution to the proportion is \( x = 2 \).
Therefore, the correct answer is b. 2.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve the proportion \(\frac{x-1}{2}=\frac{x+2}{8}\), we can cross-multiply: \[ 8(x-1) = 2(x+2) \] Expanding both sides gives: \[ 8x - 8 = 2x + 4 \] Now, we can isolate \(x\) by moving \(2x\) to the left side and \(8\) to the right side: \[ 8x - 2x = 4 + 8 \\ 6x = 12 \] Dividing both sides by 6 gives: \[ x = 2 \] So the answer is \(2\) (option b).
