# Linear Equations in One Variable on the SAT: Examples & Practice Source: https://1600.now/sat-skill/linear-equations-one-variable --- Math · Algebra ## Linear Equations in One Variable Keep an equation balanced: simplify each side, collect the variable terms, and undo multiplication or division. Substitute the result into the original equation before answering. Written by [Luke Finigan](https://1600.now/about) 2 min read Updated Oct 2, 2026 ### 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 Try it yourself: What is $x$ if $4(x-2)=2x+10$? · A $1$ B $5$ C $9$ D $18$ ### Sample linear equations in one variable questions Linear Equations in One Variable · Easy: If $6x = 11$, what is the value of $24x$? · A 6 B 15 C 44 D 59 - [Open the question and explanation](https://1600.now/bank/math/d2aa08c6) Linear Equations in One Variable · Easy: If $8+x=5$, what is the value of $-24-3x$? · A $-15$ B $-3$ C $5$ D $33$ - [Open the question and explanation](https://1600.now/bank/math/a17354ac) Linear Equations in One Variable · Easy: If $x-3=4$, what is the value of $3(x-3)$? · A 4 B 10 C 12 D 24 - [Open the question and explanation](https://1600.now/bank/math/b156f9e1) ### 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. [Practice linear equations in one variable](https://1600.now/bank/math/skill/Linear%20equations%20in%20one%20variable) [Print the linear equations in one variable worksheet and worked answers](https://1600.now/sat-linear-equations-one-variable-worksheet). Then use a [mixed practice module](https://1600.now/modules) to check whether you can choose this method among other question types. ### Source and question labels The bank label for this guide is "Linear equations in one variable" in Algebra. The worked examples above are written for this guide. - [College Board: Types of Math tested](https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types) ### Related skills - **[Linear Inequalities](https://1600.now/sat-skill/linear-inequalities)** Solve inequalities like equations, but reverse the comparison when multiplying or dividing by a negative number. - **[Systems of Linear Equations](https://1600.now/sat-skill/systems-of-linear-equations)** A solution to a system must satisfy both equations. - **[Equivalent Expressions](https://1600.now/sat-skill/equivalent-expressions)** Equivalent expressions give the same value for every input where both are defined.