Linear Equations in One Variable

Isolate the variable without losing a sign

A linear equation has the variable to the first power. For $3(2x-5)=4x+7$, distribute the entire 3: $6x-15=4x+7$. Subtract $4x$ from both sides, add 15, and divide by 2. The result is $x=11$.

Check the original sides: $3(22-5)=51$ and $44+7=51$. Checking the simplified equation alone would not catch a distribution error made earlier.

Clear fractions with one multiplication

For $\frac{x}{3}+\frac{x-2}{6}=4$, multiply every term by 6. That produces $2x+x-2=24$, so $3x=26$ and $x=\frac{26}{3}$. A fractional answer is allowed; do not round unless the question requests it.

Keep the numerator grouped. Multiplying $\frac{x-2}{6}$ by 6 gives $x-2$, not $x-12$. Write the full cleared equation before combining terms.

Recognize no solution and infinitely many solutions

The equation $2(x+3)=2x+6$ simplifies to $6=6$. Every real value of $x$ works. By contrast, $2(x+3)=2x+7$ simplifies to $6=7$, so no value works.

When a question asks for a coefficient that gives infinitely many solutions, match both the variable coefficient and the constant after simplifying. Matching just the coefficient can instead produce parallel expressions that never equal each other.

Answer the expression the question asks for

If the stem asks for $2x+1$, stop once you can identify that expression. From $5(2x+1)=35$, divide by 5 to get $2x+1=7$. Solving for $x$ adds a step without changing the requested answer.

For a miss, label the exact step: distribution, denominator clearing, sign, or requested expression. That label tells you which operation to repeat in your next drill.

Check your understanding

Sample linear equations in one variable questions

Practice this skill

1. Solve a small batch with the original equation visible beside your steps.
2. Substitute every result; for an identity or contradiction, explain why there is no single solution.
3. Redo a missed equation with different numbers, then mix it with other Algebra questions.

Print the linear equations in one variable worksheet and worked answers.

Then use a mixed practice module to check whether you can choose this method among other question types.