Linear Equations in One Variable
Master solving equations with one unknown. Foundation for all algebra.
Practice Problems
Solve for x: 3x + 7 = 22
Subtract 7 from both sides
Divide both sides by 3
Check: 3(5) + 7 = 15 + 7 = 22 ✓
5x - 8 = 22
3(2x - 4) = 18
Common Mistakes
Pro Tips & Shortcuts
SAT Tip: Expect 2-3 questions like this. Should take <30 seconds each.
SAT Tip: On the SAT, linear equations often appear in word problems. Always define your variable clearly before setting up the equation.
SAT Tip: Think of an equation as a balanced scale. Any operation must be performed on both sides to keep it balanced.
SAT Tip: On the SAT, always check if your answer makes sense in the context. If solving for age and you get -5, you made an error!
SAT Tip: This type of equation appears frequently on the SAT. Practice until you can solve it in under 30 seconds.
SAT Tip: Distribution errors are among the most common mistakes on the SAT. Double-check your signs, especially with negatives!
For simple equations, work backwards from the answer choices - plug them in!
If you see fractions, multiply both sides by the LCD (Least Common Denominator) to clear them immediately - this saves time and reduces errors.
Combine operations when possible: instead of subtracting 5 then dividing by 2, think '(x - 5)/2' mentally.
For simple equations like 2x + 5 = 17, do mental math: subtract 5 (get 12), divide by 2 (get 6). Save time!
Notice the pattern: 'undo' operations in reverse order (PEMDAS backwards). Subtraction → Addition, Multiplication → Division.
Alternative method: Divide both sides by 3 first → 2x - 4 = 6, then solve. Sometimes this is faster!
Use Desmos to verify answers quickly.