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 combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality -4a ≤ -28?

Back

Divide both sides by -4, remembering to flip the inequality sign: a ≥ 7.

Front

What does it mean to graph the solution set of an inequality?

Back

Graphing the solution set involves drawing a number line and shading the region that represents all possible solutions to the inequality.

Front

What is the solution to the inequality 14 < -2a + 6 - 2a?

Back

The solution is a < -2.

Front

How do you isolate the variable in the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides to get -4x ≤ 40, then divide by -4 (flipping the inequality) to find x ≥ -10.

Front

What is the first step in solving the inequality 28 - k ≥ 7(k - 4)?

Back

Distribute the 7 on the right side: 28 - k ≥ 7k - 28.

Front

What does the inequality p ≥ 20 represent?

Back

It represents all values of p that are greater than or equal to 20.

Front

How do you check if a solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it makes the inequality true.

Front

What is the significance of flipping the inequality sign when multiplying or dividing by a negative number?

Back

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

Front

What is the solution to the inequality 28 - k ≥ 7(k - 4)?

Back

The solution is k ≤ 7.