Two Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 22 < 6c + 4?

Back

To solve 22 < 6c + 4, first subtract 4 from both sides to get 18 < 6c, then divide both sides by 6 to find c > 3.

Front

What does the inequality a ≥ 11 represent graphically?

Back

The inequality a ≥ 11 represents all values of a that are greater than or equal to 11, which is shown as a closed circle on 11 and a line extending to the right on a number line.

Front

How do you determine which graph corresponds to a given inequality?

Back

To determine which graph corresponds to a given inequality, analyze the inequality's direction (greater than or less than) and whether it includes equality (≥ or ≤) to identify the correct representation.

Front

What is the solution to the inequality 2x - 1 > 5?

Back

To solve 2x - 1 > 5, add 1 to both sides to get 2x > 6, then divide by 2 to find x > 3.

Front

What does the inequality 25 < X - 10 mean?

Back

The inequality 25 < X - 10 means that X must be greater than 35, as adding 10 to both sides gives X > 35.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (>, <) do not include the boundary value, while non-strict inequalities (≥, ≤) include the boundary value.

Front

How do you graph the inequality x < 4?

Back

To graph x < 4, draw a number line, place an open circle on 4, and shade to the left to indicate all values less than 4.

Front

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

Back

The first step in solving a two-step inequality is to isolate the term with the variable by performing the inverse operation (addition or subtraction) on both sides.

Front

How do you check your solution for an inequality?

Back

To check your solution for an inequality, substitute the solution back into the original inequality to see if it holds true.