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

What does |x| < a mean?

Back

It means that x is within a distance of a from 0, or -a < x < a.

Front

What does |x| > a mean?

Back

It means that x is outside the distance of a from 0, or x < -a or x > a.

Front

How do you solve |x + 3| < 5?

Back

You set up two inequalities: -5 < x + 3 < 5, which simplifies to -8 < x < 2.

Front

How do you solve |x - 4| ≥ 3?

Back

You set up two inequalities: x - 4 ≥ 3 or x - 4 ≤ -3, which simplifies to x ≥ 7 or x ≤ 1.

Front

What is the solution to |y - 2| < 0?

Back

There is no solution, as absolute values cannot be negative.

Front

What is the solution to |x| ≤ 4?

Back

The solution is -4 ≤ x ≤ 4.

Front

What does the inequality 3|x| + 2 < 11 represent?

Back

It represents the values of x that are within a certain range after isolating the absolute value.

Front

How do you interpret |x| = a?

Back

It means x can be either a or -a.

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.