Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An inequality that involves the absolute value of a variable, expressing a range of values that satisfy the condition.

Front

How do you solve the inequality |x + 4| + 8 > 2?

Back

All real numbers are solutions.

Front

What does the solution |c + 4| < 5 represent?

Back

The solution is -9 < c < 1, meaning c is between -9 and 1.

Front

What is the meaning of |y - 4| ≥ 8?

Back

It means y is either less than or equal to -4 or greater than or equal to 12.

Front

How do you interpret the inequality |3c - 4| < 12?

Back

The solution is -2 2/3 < c < 5 1/3, meaning c is between -2 2/3 and 5 1/3.

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 it mean if an absolute value inequality has no solution?

Back

It means there are no values of the variable that satisfy the inequality.

Front

How do you express the solution to |x| < a?

Back

The solution is -a < x < a.

Front

What is the difference between |x| > a and |x| < a?

Back

|x| > a means x is outside the interval (-a, a), while |x| < a means x is inside that interval.

Front

What is the graphical representation of |x| < a?

Back

It is represented by an open interval on the number line between -a and a.