Virginia SOL Math / Grade 8 / Patterns, Functions & Algebra

8.PFA.5

Multistep Linear Inequalities

What you'll learn

  • Write multistep linear inequalities in one variable
  • Solve inequalities and graph the solution on a number line
  • Solve practical problems using inequalities

Words to know

Inequality —
a statement comparing expressions with <, >, less-or-equal, or greater-or-equal
Solution set —
all values that make an inequality true
Boundary —
the value where the inequality changes from true to false
Reverse the symbol —
flip the inequality when multiplying or dividing by a negative
Number line —
a line used to graph a solution set

Why it matters Inequalities model limits and ranges, such as a budget, a minimum score, or a maximum weight, where many values can work.

Worked examples

Model ItI do

Solve 2x + 3 > 11.

Subtract 3 from both sides: 2x > 8. Divide both sides by 2: x > 4. The solution set is all numbers greater than 4.

Try It TogetherWe do

Solve -3x < 12.

Divide both sides by -3. Because we divided by a negative, reverse the symbol: x > -4.

Now YouYou do

Solve 4x - 5 less-or-equal 11.

Undo the subtraction, then the multiplication, keeping the symbol since you divide by a positive. 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 + 4 < 9.

  2. 2.Solve 2x > 10.

  3. 3.Solve x - 3 greater-or-equal 2.

On Level

The core Quick Check from the book.

  1. 1.Solve x + 6 < 10.

  2. 2.Solve 3x greater-or-equal 15.

  3. 3.Solve 2x - 1 > 7.

  4. 4.Solve -2x > 8.

  5. 5.Solve 5x + 2 less-or-equal 17.

Challenge

Stretch your thinking.

  1. 1.Solve 3x - 4 less-or-equal 11.

  2. 2.Solve -4x > 20.

  3. 3.A student needs at least 90 total points from a 40-point quiz and a test worth x points. Write and solve an inequality for the test points needed.