Solving & Graphing Inequalities Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

How do you solve the inequality -2x + 1 < 7?

Back

To solve -2x + 1 < 7, subtract 1 from both sides to get -2x < 6, then divide by -2 (remember to flip the inequality sign) to find x > -3.

Front

What does the solution set x > -3 represent on a number line?

Back

The solution set x > -3 represents all numbers greater than -3, which is shown as an open circle at -3 and a line extending to the right.

Front

What is the meaning of the inequality b ≤ -2?

Back

The inequality b ≤ -2 means that b can be any number less than or equal to -2.

Front

How do you graph the inequality 5w ≥ 30?

Back

To graph 5w ≥ 30, first solve for w by dividing both sides by 5 to get w ≥ 6. Then, plot a closed circle at 6 and shade to the right.

Front

What does a closed circle on a number line indicate?

Back

A closed circle indicates that the number is included in the solution set (≤ or ≥).

Front

What does an open circle on a number line indicate?

Back

An open circle indicates that the number is not included in the solution set (< or >).

Front

How do you solve the inequality x - 3 > -3?

Back

To solve x - 3 > -3, add 3 to both sides to get x > 0.

Front

What is the solution set for the inequality x - 3 > -3?

Back

The solution set for x - 3 > -3 is all numbers greater than 0, represented as (0, ∞) on a number line.

Front

What is the first step in solving an inequality?

Back

The first step in solving an inequality is to isolate the variable on one side of the inequality.