3.3.2 Flashcardizz: Two-Step Inequalities: Advanced

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. For example, in the inequality 2x + 3 < 7, you would first subtract 3 from both sides and then divide by 2.

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Back

1. Distribute: -24 < 32x + 40 2. Subtract 40: -64 < 32x 3. Divide by 32: -2 < x or x > -2.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either smaller than or equal to the value on the right.

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Back

1. Simplify: 3x ≤ -9 2. Divide by 3: x ≤ -3.

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Back

Distribute the 3: -6x + 27 ≤ -27.

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Back

1. Subtract 27 from both sides: -6x ≤ -54 2. Divide by -6 (remember to flip the inequality): x ≥ 9.

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Back

1. Multiply both sides by 4: x - 46 > -48 2. Add 46: x > -2.

Front

What does it mean to 'match the inequality with the corresponding graph'?

Back

It means to find the graph that accurately represents the solution set of the inequality, showing the range of values that satisfy it.

Front

What is the importance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains true.