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 the equation |x| = a represent?

Back

It represents two possible equations: x = a and x = -a, where a is a non-negative number.

Front

What does the inequality |x| < a mean?

Back

It means that x is within a distance of a from zero, resulting in the compound inequality -a < x < a.

Front

What does the inequality |x| > a mean?

Back

It means that x is more than a distance of a from zero, resulting in the compound inequalities x < -a or x > a.

Front

How do you solve the equation |x - 3| = 5?

Back

Set up two equations: x - 3 = 5 and x - 3 = -5. Solve to find x = 8 and x = -2.

Front

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

Back

Solve the compound inequalities: -3 < 2x + 1 < 3, resulting in -2 < x < 1.

Front

What is the graph of y = |x|?

Back

It is a V-shaped graph that opens upwards, with the vertex at the origin (0,0).

Front

What transformations occur in the graph of y = |x + 2| + 2?

Back

The graph shifts left 2 units and up 2 units from the parent function y = |x|.

Front

Can an absolute value equal a negative number?

Back

No, an absolute value cannot equal a negative number.

Front

What is the solution to the equation |−2n| + 10 = −50?

Back

No Solution, because the left side is always non-negative.