Solving Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

Front

What does 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' means that at least one of the conditions must be true.

Front

How do you solve a compound inequality with 'and'?

Back

To solve a compound inequality with 'and', solve each inequality separately and find the intersection of the solutions.

Front

How do you solve a compound inequality with 'or'?

Back

To solve a compound inequality with 'or', solve each inequality separately and combine the solutions.

Front

What is the solution to the inequality x > 2 or x ≤ -3?

Back

The solution is all values of x that are greater than 2 or less than or equal to -3.

Front

How do you graph the inequality x > 2?

Back

Graph a number line, place an open circle at 2, and shade to the right.

Front

How do you graph the inequality x ≤ -3?

Back

Graph a number line, place a closed circle at -3, and shade to the left.

Front

What is the solution to the compound inequality -8 < 2(x + 4) or -3x + 4 > x - 4?

Back

The solution is x > -8 or x < 2.

Front

What is the solution to the compound inequality -3 ≤ 2x - 1 ≤ 5?

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The solution is -1 ≤ x ≤ 3.