📝 Linear Equations

Part 1 of 7 — Linear Equations Basics

A linear equation has the form ax + b = c, where x is the variable.

To solve, isolate x by performing inverse operations on both sides.

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Key Insight: The solution is the value that makes the equation true.

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

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Solving Multi-Step Equations

Part 2 of 7 — Solving Multi-Step Equations

Multi-step equations require multiple operations to isolate x.

Always simplify each side first: distribute and combine like terms.

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Key Insight: Apply inverse operations in reverse order of operations.

SAT Tip: Example: 3(2x - 4) + 5 = 23 → 6x - 12 + 5 = 23 → 6x = 30 → x = 5.

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Linear Inequalities

Part 3 of 7 — Linear Inequalities

Inequalities use <, >, ≤, ≥ instead of =.

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

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Key Insight: Graph solutions on a number line.

SAT Tip: Compound inequalities: -3 < 2x + 1 ≤ 7 — solve both parts.

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Systems of Linear Equations

Part 4 of 7 — Systems of Linear Equations

A system has two or more equations with the same variables.

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

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Key Insight: Elimination: add/subtract equations to eliminate a variable.

SAT Tip: No solution: parallel lines (same slope, different intercept); infinite solutions: same line.

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Word Problem Setup

Part 5 of 7 — Word Problem Setup

Read the problem carefully — identify what x represents.

Translate words to math: "is" = equals, "more than" = addition, "of" = multiplication.

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Key Insight: Set up the equation, then solve.

SAT Tip: Always check: does your answer make sense in context?.

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Problem-Solving Workshop

Part 6 of 7 — Problem-Solving Workshop

Read the problem carefully — identify what x represents.

Translate words to math: "is" = equals, "more than" = addition, "of" = multiplication.

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Key Insight: Set up the equation, then solve.

SAT Tip: Always check: does your answer make sense in context?.

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Review & Applications

Part 7 of 7 — Review & Applications

Read the problem carefully — identify what x represents.

Translate words to math: "is" = equals, "more than" = addition, "of" = multiplication.

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Key Insight: Set up the equation, then solve.

SAT Tip: Always check: does your answer make sense in context?.

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Match the Concepts 🔍