Concept Byte: Modeling Multi-Step Inequalities

Use With Lesson 3-4

ACTIVITY

Sometimes you need to perform two or more steps to solve an inequality. Models can help you understand how to solve multi-step inequalities.

Activity

Model and solve 2 x − 3 < 1 . 2 x minus 3 less than 1 .

Inequality	Model	Think
2 x − 3 < 1 2 x minus 3 less than 1		The tiles model the inequality.
2 x − 3 + 3 < 1 + 3 2 x minus 3 plus 3 less than 1 plus 3		Add 3 yellow tiles to each side.
2 x < 4 2 x less than 4		Simplify by removing the zero pairs.
2 x 2 < 4 2 fraction 2 x , over 2 end fraction , less than , 4 halves		Divide each side into two equal groups.
x < 2 x less than 2		Each green tile is less than two yellow tiles, so x < 2 . x less than 2 .

Exercises

Write an inequality for each model. Use tiles to solve each inequality.

Use tiles to model and solve each inequality.

3. 2 n − 5 ≥ 3 2 n minus 5 greater than or equal to 3
4. − 9 > 4 x − 1 negative 9 greater than 4 x minus 1
5. 3 w + 4 < − 5 3 w plus 4 less than negative 5
6. z + 6 ≤ 2 z + 2 z plus 6 less than or equal to 2 z plus 2
7. 3 m + 7 ≥ m − 5 3 m plus 7 greater than or equal to m minus 5
8. 5 b + 6 > 3 b − 2 5 b plus 6 greater than 3 b minus 2

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