What you’ll learn
Solve linear equations with fractional coefficients.
Key idea
Distribute the negative grouped term with both signs intact; then isolate the nonzero combined x coefficient.
Clear every fraction with a common multiplier and retain both grouped signs; verify exact solutions in the original equation.
Worked example
Enter the exact value or ordered values in the format requested below.
Solve (x+2)/2-(x-3)/3=9/4; enter exact numerical x as integer, fraction or equivalent decimal.
- Multiply every term by common multiple 6: 3(x+2)-2(x-3)=27/2.
- Correct distribution gives coefficient 1 and constant 12; 1x+12=27/2, so x=3/2. Substitution in the original verifies the exact value.
Answer: 3/2
Quick Check
Evaluate a worked attempt at solve linear equations with fractional coefficients, identify the first invalid step, and provide the correction.
Solve (x+3)/2-(x-3)/3=3: Step 1 clears denominators to 3(x+3)-2(x-3)=18. Step 2 expands the second product as -2x-6, concludes x=15. Locate the first invalid step and correct x.