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 and Graph Inequalities — Get the letter alone, then show all answers on a line.
• Solve — Find the number that makes it true.
• Graph — Show answers on a number line.
• Solution — A value that makes the math sentence true.
• Substitute — Put a number in place of a letter.
• Solution set — All the values that make the sentence true.
• Inverse operation — Two 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 + 8 > 15

Check your answer

x > 7; open circle at 7, shade right

Subtract 8 from both sides: x > 15 − 8 = 7. Open circle at 7 (not included), shade right. ✓

Sentence starter

I know ___ because ___.

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