Compound Inequalities /Absolute Value Inequalities PRACTICE GAME

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'. For example, x < 5 and x > 1.

Front

What does |x| represent?

Back

|x| represents the absolute value of x, which is the distance of x from 0 on the number line, always non-negative.

Front

How do you solve an absolute value equation like |x| = a?

Back

To solve |x| = a, set up two equations: x = a and x = -a.

Front

What is the solution to the equation -|−2r − 1| = 11?

Back

No Solution, because the left side is always non-positive and cannot equal 11.

Front

How do you solve an inequality like 3|2x + 7| + 7 < 4?

Back

First, isolate the absolute value: 3|2x + 7| < -3. Since absolute values are non-negative, this has no solution.

Front

What does the inequality -5|x - 4| > 20 imply?

Back

This implies |x - 4| < -4, which has no solution since absolute values cannot be negative.

Front

What is the solution to the equation −2|−2r − 4| = -12?

Back

{-5, 1}, because you can isolate the absolute value and solve for r.

Front

How do you interpret the solution t < -2 or t > 5?

Back

This means t can be any number less than -2 or any number greater than 5.

Front

What is the first step in solving an absolute value inequality?

Back

Isolate the absolute value expression on one side of the inequality.

Front

What does the solution set x < -3 and x > -5/3 represent?

Back

This represents all values of x that are less than -3 and greater than -5/3, which is an empty set.