Solving Compound Inequalities

Front

When solving inequalities, what must you do to the inequality when multiplying or dividing by a negative?

Back

Flip the inequality.

Front

What does the inequality x > 2 or x ≤ -3 represent on a number line?

Back

It represents values greater than 2 or less than or equal to -3.

Front

Write an inequality for the graph that shows values from -2 to 5, including -2 but not 5.

Back

-2 ≤ x < 5

Front

Solve the inequality: 3x + 2 < -4 or 4x + 4 > 24.

Back

x < -2 or x > 5.

Front

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

Back

x < -8 or x < 2.

Front

What is a compound inequality?

Back

An inequality that combines two simple inequalities using 'and' or 'or'.

Front

What does 'and' mean in a compound inequality?

Back

Both conditions must be true for the solution to be valid.

Front

What does 'or' mean in a compound inequality?

Back

At least one of the conditions must be true for the solution to be valid.

Front

How do you graph the compound inequality x > 2 and x < 5?

Back

Draw a number line and shade the region between 2 and 5, not including the endpoints.

Front

What is the first step in solving the compound inequality 2x - 3 < 5 and x + 1 > 2?

Back

Solve each inequality separately.