Solve the fractional equation and keep an exact answer.
3x+1−2x−2=1
1
Clear both denominators
Multiply every term by 6, including each complete numerator.
2(x+1)−3(x−2)=6
2
Distribute before collecting
The negative 3 changes the sign of both terms in x minus 2.
2x+2−3x+6=6
3
Solve and verify
Combining like terms gives x = 2, so rechecking exposes that this example must be solved carefully.
−x+8=6⇒x=2
4
Substitute into the original
At x = 2, the first fraction is 1 and the second is 0.
32+1−22−2=1
Answer
x=2
Study plan
Use mistakes to choose the next problem
Use the first wrong line to choose the repair. Repeat a similar problem only after naming why that line changed the solution set.
Secure signed arithmetic
Write every distributed term before combining. A missed negative sign often survives unnoticed until the final answer.
Keep equations balanced
Annotate the operation applied to both sides, especially when clearing denominators or moving variable terms.
Recognize special outcomes
When x cancels, decide whether the remaining statement is always true or always false.
Verify in the original form
Substitution catches distribution and denominator errors that a simplified line can hide.
Common questions
Practice linear equations one clear step at a time FAQ
What should I do first when solving a linear equation?
Simplify each side independently. Distribute, combine like terms, and clear fractions if that makes the structure easier to see. Then collect the variable terms and constants using balanced operations.
Why must I apply an operation to both sides?
An equation states that two expressions have the same value. Applying the same reversible operation to both sides preserves that equality and therefore preserves the solution set.
How do I know whether an equation has no solution or infinitely many solutions?
Simplify both sides. If the variable terms cancel and leave a false statement, there is no solution. If they leave a true identity, every permitted real value is a solution.
Should I use decimals or fractions in my answer?
Keep exact fractions when the division does not terminate. A decimal is useful as an approximation, but substitution with the exact value avoids rounding ambiguity.
How can I check a linear equation answer?
Substitute the value into both sides of the original equation. Simplify each side separately and confirm that they produce the same number.
Sources and curriculum alignment
This page follows standard introductory mathematics notation and learning sequences. Use these references to continue with a complete course treatment.
