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

How do you solve the compound inequality -6 < 3x + 9 < 21?

Back

First, isolate the variable by solving the two inequalities separately: 1) -6 < 3x + 9 and 2) 3x + 9 < 21.

Front

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

Back

You must flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number.

Front

What is the solution set for the inequality -2 ≤ x < 5?

Back

The solution set includes all real numbers x such that x is greater than or equal to -2 and less than 5.

Front

When is it necessary to change the sign of an inequality?

Back

You change the sign of an inequality when multiplying or dividing by a negative number.

Front

What does the 'and' in a compound inequality signify?

Back

The 'and' signifies that both conditions must be true at the same time for the solution to be valid.

Front

What does the 'or' in a compound inequality signify?

Back

The 'or' signifies that at least one of the conditions must be true for the solution to be valid.

Front

How do you graph the inequality -2 ≤ x < 5?

Back

You would shade the number line starting from -2 (including -2) to 5 (not including 5), using a closed dot at -2 and an open dot at 5.

Front

What is the first step in solving the compound inequality 2x - 3 < 5 and x + 4 > 2?

Back

The first step is to solve each inequality separately: 1) 2x - 3 < 5 and 2) x + 4 > 2.

Front

What is the solution to the inequality 3x + 6 > 0?

Back

The solution is x > -2.