Lesson 6: Solve and Graph Inequalities6.AT.8

I can…

I can solve an inequality and graph its solution set on a number line.

Key words

• Solve — To find the number that makes it true.
• Graph — To show answers on a number line with circles and shading.
• Solution — A number that makes the equation or inequality true.
• Substitute — To put a number in place of a letter.
• Solution set — All the numbers that make the inequality true.
• Inverse operation — Two math actions that undo each other, like × and ÷.

Steps

1. Solve x + 3 > 53. The inverse of adding 3 is subtracting 3.
2. I subtract 3 from both sides: x + 3 − 3 > 53 − 3, so x > 50.
3. The symbol > does not include 50, so I use an open circle at 50.
4. 'Greater than' shades right. Check: x = 60 gives 60 + 3 = 63 > 53. True!

Try it

Solve and describe the graph: x + 5 < 11

Check your answer

x < 6; open circle at 6, shade left

Subtract 5 from both sides: x < 11 − 5 = 6. Open circle at 6 (not included), shade left. ✓

Sentence starter

I know ___ because ___.

Goal: I can explain my work using the words solve, graph, solution, and substitute.