Solving Multi-Step Inequalities

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, or division.

Front

How do you solve the inequality -3 - 6(4x + 6) > -111?

Back

First, distribute -6: -3 - 24x - 36 > -111. Then combine like terms: -24x - 39 > -111. Add 39 to both sides: -24x > -72. Finally, divide by -24 (remember to flip the inequality): x < 3.

Front

What is the inequality for when Cell plan A is greater than Cell plan B?

Back

40 + 0.04x > 30 + 0.09x.

Front

How do you solve the inequality 12 ≥ 15 - 6y?

Back

Subtract 15 from both sides: -3 ≥ -6y. Divide by -6 (flip the inequality): y ≥ ½.

Front

What inequality represents when Sue's lunch account is more than Troy's?

Back

25 - 2.5d > 50 - 3.25d.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Divide by -4 (flip the inequality): x ≥ -10.

Front

What does it mean to check your solution set in inequalities?

Back

Checking your solution set means substituting your solution back into the original inequality to ensure it holds true.

Front

What is the first step in solving a multi-step inequality?

Back

The first step is to simplify the inequality by distributing and combining like terms if necessary.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.