ACT Math · Study Guide
Elementary Algebra
Master solving linear equations, inequalities, and absolute value equations. The most common algebra question types on the ACT.
About 50 minutes to master
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What you'll learn
- Solve one-variable and two-variable linear equations
- Solve and graph linear inequalities on a number line
- Interpret slope-intercept form (y = mx + b) and point-slope form
- Solve absolute value equations and inequalities
- Translate word problems into linear equations
Key concepts
Linear equations produce straight lines when graphed. In slope-intercept form y = mx + b, m is the slope (rise/run) and b is the y-intercept. To solve a linear equation, isolate the variable by performing the same operation on both sides. For inequalities, remember to flip the inequality sign when multiplying or dividing by a negative number. Absolute value equations |ax + b| = c split into two cases: ax + b = c and ax + b = −c. Around 15-20% of ACT Math questions involve linear equations or their applications.
Pro tips
- When a problem gives two points, find the slope first: m = (y₂ − y₁) / (x₂ − x₁).
- For inequality word problems, translate 'at most' as ≤ and 'at least' as ≥.
- If an absolute value equation equals a negative number, there is no solution. The ACT tests this.
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