📋 Algebra Equations

Part 1 of 7 — Linear Equations

Isolate the variable using inverse operations.

Multi-step: distribute, combine like terms, then isolate.

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Key Insight: Variables on both sides: move all variable terms to one side.

ACT Tip: Check your answer by substituting back into the original equation.

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Inequalities

Part 2 of 7 — Inequalities

Solve like equations, but flip the inequality sign when multiplying/dividing by a negative.

Graph solutions on a number line: open circle for < or >, closed for ≤ or ≥.

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Key Insight: Compound inequalities: AND (intersection) vs. OR (union).

ACT Tip: ACT may present inequalities in word problem form.

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Systems of Equations

Part 3 of 7 — Systems of Equations

Substitution: solve one equation for a variable, plug into the other.

Elimination: add/subtract equations to cancel a variable.

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Key Insight: Special cases: no solution (parallel lines) or infinite solutions (same line).

ACT Tip: ACT tip: if the system looks complex, try elimination first.

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Absolute Value

Part 4 of 7 — Absolute Value

|x| = a means x = a or x = -a.

|x| < a means -a < x < a (AND compound inequality).

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Key Insight: |x| > a means x > a or x < -a (OR compound inequality).

ACT Tip: Always isolate the absolute value expression first before splitting into cases.

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Word Problem Translation

Part 5 of 7 — Word Problem Translation

Assign variables to unknowns.

"Is" = equals, "more than" = addition, "less than" = subtraction.

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Key Insight: "Of" = multiplication, "per" = division.

ACT Tip: Set up the equation, solve, then verify your answer makes sense in context.

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Problem-Solving Workshop

Part 6 of 7 — Problem-Solving Workshop

Assign variables to unknowns.

"Is" = equals, "more than" = addition, "less than" = subtraction.

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Key Insight: "Of" = multiplication, "per" = division.

ACT Tip: Set up the equation, solve, then verify your answer makes sense in context.

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Review & Applications

Part 7 of 7 — Review & Applications

Assign variables to unknowns.

"Is" = equals, "more than" = addition, "less than" = subtraction.

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Key Insight: "Of" = multiplication, "per" = division.

ACT Tip: Set up the equation, solve, then verify your answer makes sense in context.

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