One-Variable Inequalities

Learn and apply one-variable inequalities using equations, examples, and interpretation.

Lesson 1 of 53 parts Practice Flashcards

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Inequality Symbols

Objective: Explain and use inequality symbols in an Algebra 1 problem.

The symbols <, >, ≤, and ≥ compare values and define sets of possible solutions rather than a single required value. When the symbol contains an equality bar.

Worked examples

Try itExample 1.1: Solve 4x+14<34.Show answer

x<5. Subtract 14, then divide by positive 4; the sign stays the same. The answer is x<5.

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Inequality Symbols

Objective: Explain and use inequality symbols in an Algebra 1 problem.

The symbols <, >, ≤, and ≥ compare values and define sets of possible solutions rather than a single required value. When the symbol contains an equality bar.

Worked examples

Try itExample 1.1: Solve 4x+14<34.Show answer

x<5. Subtract 14, then divide by positive 4; the sign stays the same. The answer is x<5.

Solving by Addition

Objective: Explain and use solving by addition in an Algebra 1 problem.

Adding or subtracting the same number on both sides preserves the direction of an inequality. Both values move by the same amount.

Worked examples

Try itExample 2.1: Solve 2x+24<40.Show answer

x<8. Subtract 24, then divide by positive 2; the sign stays the same. The answer is x<8.

Multiplying by a Negative

Objective: Explain and use multiplying by a negative in an Algebra 1 problem.

Multiplying or dividing an inequality by a negative reverses its direction: if a<b, then −a>−b. When both sides are multiplied or divided by a negative number.

Worked examples

Try itExample 3.1: Solve −3x+34<1.Show answer

x>11. Subtract 34, then divide by negative 3; reverse the sign. The answer is x>11.

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