Multistep inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division on both sides.

Front

How do you isolate a variable in a multistep inequality?

Back

To isolate a variable, perform inverse operations on both sides of the inequality, ensuring to maintain the direction of the inequality unless multiplying or dividing by a negative number.

Front

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

Back

The direction of the inequality sign reverses when you multiply or divide both sides by a negative number.

Front

What is the solution to the inequality -138 ≥ -6(6b − 7)?

Back

b ≥ 5.

Front

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

Back

First, distribute -6, then combine like terms, and isolate x to find x < 3.

Front

What is the solution to the inequality 5(6 + 3r) + 7 ≥ 127?

Back

r ≥ 6.

Front

What does the inequality y > x represent graphically?

Back

It represents the region above the line y = x in a coordinate plane.

Front

How do you solve the inequality -p − 4p > -10?

Back

Combine like terms to get -5p > -10, then divide by -5, reversing the inequality to find p < 2.

Front

What is the first step in solving a multistep inequality?

Back

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

Front

What is the importance of checking your solution in a multistep inequality?

Back

Checking your solution ensures that it satisfies the original inequality and helps to confirm that no errors were made during the solving process.