2.4 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 4(2a + 3) < 3(a - 1)?

Back

First, distribute: 8a + 12 < 3a - 3. Then, subtract 3a from both sides: 5a + 12 < -3. Next, subtract 12: 5a < -15. Finally, divide by 5: a < -3.

Front

What does the inequality x/2 - 6 < -8 represent?

Back

To solve, add 6 to both sides: x/2 < -2. Then, multiply by 2: x < -4.

Front

Match the graph with the inequality 4(b+3) - 6 ≤ -2.

Back

The graph that shows a closed circle at -2 and shading to the left represents this inequality.

Front

What does the inequality -2 ≥ n mean?

Back

It means that n can be any number less than or equal to -2.

Front

How do you solve the inequality 6 - 11b ≤ -3?

Back

Subtract 6 from both sides: -11b ≤ -9. Then, divide by -11 (remember to flip the inequality): b ≥ 9/11.

Front

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

Back

The first step is to simplify both sides of the inequality, if possible, by distributing and combining like terms.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

How can you check your solution to an inequality?

Back

You can check by substituting a value from the solution set back into the original inequality to see if it holds true.

Front

What is the solution set of the inequality x/3 + 10 ≤ -2?

Back

To solve, subtract 10 from both sides: x/3 ≤ -12. Then, multiply by 3: x ≤ -36.