Solving and Graphing Compound Inequalities

Front

What is a compound inequality?

Back

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

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 does it mean to 'flip' an inequality?

Back

To 'flip' an inequality means to reverse the inequality sign, which occurs when multiplying or dividing both sides by a negative number.

Front

Solve the compound inequality: -8 < 2(x + 4) or -3x + 4 > x - 4.

Back

x > -8 or x < 2.

Front

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

Back

x < -2 or x > 5.

Front

Solve the compound inequality: 3x - 4 < -13 or 7x + 1 > 22.

Back

x < -3 or x > 3.

Front

Can x = 3 be a solution to the inequality 6 < x + 5 ≤ 11?

Back

Yes.

Front

What must you do when solving inequalities and multiplying or dividing by a negative?

Back

You must flip the inequality.

Front

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

Back

The solution set includes all values less than -2 and all values greater than 5.

Front

What is the graphical representation of a compound inequality with 'or'?

Back

The graph will show two separate regions on the number line, indicating the solutions for each inequality.