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.

Front

How do you isolate a variable in a multistep inequality?

Back

To isolate a variable in a multistep inequality, perform inverse operations on both sides of the inequality, maintaining the inequality's direction 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

When you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of 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 satisfy the inequality.

Front

How do you graph a solution to an inequality on a number line?

Back

To graph a solution to an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the region that represents the solution set.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the endpoint, while a non-strict inequality (≤ or ≥) includes the endpoint.

Front

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

Back

First, distribute -6 to get -3 - 24x - 36 > -111. Then combine like terms to get -24x > -72, and finally divide by -24 to find x < 3.

Front

What is the first step in solving the inequality -p - 4p > -10?

Back

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

Front

How do you solve the inequality -138 ≥ -6(6b - 7)?

Back

Distribute -6 to get -138 ≥ -36b + 42. Then, isolate b by moving terms and dividing to find b ≥ 5.

Front

What is the solution to the inequality 8x - 52 ≤ 2(6 - 4x)?

Back

First, distribute 2 to get 8x - 52 ≤ 12 - 8x. Then, combine like terms to find 16x ≤ 64, leading to x ≤ 4.