Absolute Value Equations and Inequalities

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

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

Back

An absolute value equation has no solution when the expression inside the absolute value cannot equal a negative number.

Front

Solve for x: |6 - 2x| = -5.

Back

No solution.

Front

What is the general form of an absolute value equation?

Back

The general form is |A| = B, where A is an expression and B is a non-negative number.

Front

How do you solve an absolute value equation?

Back

To solve |A| = B, set up two equations: A = B and A = -B.

Front

Solve for x: |2x - 3| + 5 = 10.

Back

x = -1 or x = 4.

Front

What is an absolute value inequality?

Back

An absolute value inequality expresses a range of values that satisfy the condition of being within a certain distance from a point.

Front

Solve the inequality: |x - 1| < 3.

Back

-2 < x < 4.

Front

What does the graph of |x| < a look like?

Back

It is a region between -a and a on the number line.

Front

Solve for x: |3x + 4| ≤ 7.

Back

-1 ≤ x ≤ 11/3.