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 - 3| ≤ 5 represent?

Back

The solution represents all values of x that are within 5 units of 3, which is the interval -2 ≤ x ≤ 8.

Front

What is the solution to the inequality |2x - 1| < 3?

Back

The solution is -1 < x < 2.

Front

What does it mean if an absolute value equation has no solution?

Back

It means that there are no values of the variable that can satisfy the equation, such as |x| = -5.

Front

What is the graphical representation of |x| < 4?

Back

The graph is a number line with an open interval from -4 to 4, indicating all numbers between -4 and 4.

Front

How do you express the solution to |x + 2| > 6?

Back

The solution is x < -4 or x > 4.

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What is the solution to the inequality |3c - 4| < 12?

Back

The solution is -2 2/3 < c < 5 1/3.

Front

What does the inequality |y - 1| ≤ 6 represent?

Back

It represents the interval -5 ≤ y ≤ 7.