Question
Solve \( \frac{x-1}{3}-\frac{x+2}{4}=2 \) Your Answer: Answer
Ask by Cross Rodriquez. in the United States
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x=34 \)
Solution
Solve the equation \( \frac{x-1}{3}-\frac{x+2}{4}=2 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{x-1}{3}-\frac{x+2}{4}=2\)
- step1: Multiply both sides of the equation by LCD:
\(\left(\frac{x-1}{3}-\frac{x+2}{4}\right)\times 12=2\times 12\)
- step2: Simplify the equation:
\(x-10=24\)
- step3: Move the constant to the right side:
\(x=24+10\)
- step4: Add the numbers:
\(x=34\)
The solution to the equation \( \frac{x-1}{3}-\frac{x+2}{4}=2 \) is \( x=34 \).
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Simplify this solution The Deep Dive
To solve the equation \( \frac{x-1}{3}-\frac{x+2}{4}=2 \), first, we need to find a common denominator for the fractions. The least common multiple of 3 and 4 is 12. Rewriting the equation with a common denominator, we have: \[ \frac{4(x-1)}{12} - \frac{3(x+2)}{12} = 2 \] This simplifies to: \[ \frac{4(x-1) - 3(x+2)}{12} = 2 \] Now, combine the numerators: \[ 4(x-1) - 3(x+2) = 4x - 4 - 3x - 6 = x - 10 \] So we rewrite the equation as: \[ \frac{x - 10}{12} = 2 \] To eliminate the fraction, multiply both sides by 12: \[ x - 10 = 24 \] Adding 10 to both sides gives: \[ x = 34 \] Thus, the solution to the equation is \( x = 34 \).
