Compound and Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which measures the distance of a number from zero on the number line.

Front

How do you solve the inequality |x| < a?

Back

To solve |x| < a, split it into two inequalities: -a < x < a.

Front

How do you solve the inequality |x| > a?

Back

To solve |x| > a, split it into two inequalities: x < -a or x > a.

Front

What does the solution x < 1 and x > -14 represent?

Back

It represents the range of values for x that are between -14 and 1, not including -14 and 1.

Front

What does the solution x < 7 or x > 9 represent?

Back

It represents the values of x that are either less than 7 or greater than 9.

Front

How do you graph the solution of a compound inequality?

Back

Graph each part of the inequality on a number line, using open circles for < and >, and closed circles for ≤ and ≥.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities using 'and' or 'or' to describe a range of values.

Front

What does the inequality 3w + 60 ≤ 1000 represent in a real-world context?

Back

It represents a budget constraint where the total cost of water bottles (3w) plus the cost of game balls (60) must not exceed $1000.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable, perform the same operations on both sides of the inequality, just like in an equation, but remember to reverse the inequality sign if you multiply or divide by a negative number.

Front

What is the solution to the inequality -3x - 8 > 16?

Back

The solution is x < -8.