Virginia SOL Math / Algebra II / Equations & Inequalities

A2.EI.1

Absolute Value Equations & Inequalities

What you'll learn

  • Solve absolute value equations with two cases
  • Solve absolute value inequalities of the 'and' and 'or' types
  • Graph the solution set on a number line

Words to know

Absolute value —
distance from 0, always 0 or positive
Case —
one of the two equations |x| = a splits into
Compound inequality —
two inequalities joined by 'and' or 'or'
Solution set —
all values that make a statement true
V graph —
the shape of an absolute value function

Why it matters Absolute value describes distance and tolerance, such as how far a measurement may vary from a target value.

Worked examples

Model ItI do

Solve |x - 1| = 3.

The expression inside can be 3 or -3, giving two cases: x - 1 = 3 or x - 1 = -3. Solving each gives x = 4 or x = -2. The V graph of y = |x - 1| meets the line y = 3 at exactly these two points.

Try It TogetherWe do

Solve |x| < 5.

This is an 'and' inequality: the distance from 0 is less than 5, so -5 < x < 5.

Now YouYou do

Solve |x + 2| = 6.

Split into two cases, then solve each. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Solve |x| = 10.

  2. 2.Solve |x - 2| = 7.

  3. 3.Solve |x| < 6.

On Level

The core Quick Check from the book.

  1. 1.Solve |x| = 8.

  2. 2.Solve |x - 3| = 5.

  3. 3.Solve |x| < 4.

  4. 4.Solve |x| > 2.

  5. 5.Solve |x + 1| = 0.

Challenge

Stretch your thinking.

  1. 1.Solve |2x - 3| = 11.

  2. 2.Solve |x + 4| > 3.

  3. 3.Solve |3x + 1| <= 8.