Virginia SOL Math / Grade 7 / Patterns, Functions & Algebra

7.PFA.4

One- and Two-Step Linear Inequalities

What you'll learn

  • Write one- and two-step inequalities from situations
  • Solve inequalities using inverse operations
  • Graph the solution of an inequality on a number line

Words to know

Inequality —
a math sentence using >, <, greater than or equal to, or less than or equal to
Solution set —
all the values that make an inequality true
Inverse operation —
an operation that undoes another
Boundary point —
the number where the solution set begins on a number line
Open circle —
a number-line mark showing a value is not included

Why it matters Inequalities describe limits and ranges, such as a budget, a minimum age, or a maximum weight, so solving them shows all the values that fit.

Worked examples

Model ItI do

Solve x + 5 > 12.

Undo the addition: subtract 5 from both sides. The solution is x > 7.

Try It TogetherWe do

Solve 2x minus 1 less than or equal to 9.

Add 1 to both sides to get 2x less than or equal to 10. Divide both sides by 2 to get x less than or equal to 5.

Now YouYou do

Solve 3x + 2 > 14.

Subtract 2 from both sides, then divide by 3. 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 x minus 2 < 6.

  3. 3.Solve 3x greater than or equal to 12.

On Level

The core Quick Check from the book.

  1. 1.Solve x minus 3 < 8.

  2. 2.Solve 4x greater than or equal to 20.

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

  4. 4.Solve x over 2 less than or equal to 5.

  5. 5.Does an open circle mean the boundary value is included?

Challenge

Stretch your thinking.

  1. 1.Solve 2x + 3 less than or equal to 11.

  2. 2.Kayla has 40 dollars. She buys a ticket for 10 dollars and snacks that cost 6 dollars each. Write and solve an inequality for how many snacks she can buy.

  3. 3.Solve 4x minus 5 > 15 and describe how to graph it.