Algebra Review: Solving Inequalities

Use With Lesson 5-6

The solutions of an inequality are all the numbers that make the inequality true. The following chart reviews the Properties of Inequality.

You can use the Addition and Multiplication Properties of Inequality to solve inequalities.

Example

Algebra Solve − 6 x + 7 > 25 . negative 6 bold italic x plus . 7 greater than 25 , .

− 6 x + 7 > 25   − 6 x > 18 Subtract  7  from each side . − 6 x − 6 < 18 − 6 Divide each side by  − 6.  Remember to reverse the inequality symbol . x < − 3 Simplify . table with 4 rows and 3 columns , row1 column 1 , negative 6 x plus 7 , column 2 greater than 25 , column 3 , row2 column 1 , negative 6 x , column 2 greater than 18 , column 3 cap subtract . 7 . fromeachside . . , row3 column 1 , fraction negative 6 x , over negative 6 end fraction , column 2 less than , 18 over negative 6 , column 3 cap divideeachsideby . minus 6. . cap remembertoreversetheinequalitysymbol . . , row4 column 1 , x , column 2 less than negative 3 , column 3 cap simplify , . , end table

Exercises

Algebra Solve each inequality.

1. 7 x − 13 ≤ − 20 7 x minus , 13 less than or equal to , minus 20
2. 3 x + 8 > 16 3 x plus . 8 greater than 16
3. − 2 x − 5 < 16 negative 2 x minus , 5 less than 16
4. 8 y + 2 ≥ 14 8 y plus . 2 greater than or equal to 14
5. a + 1 ≤ 91 eh plus . 1 less than or equal to 91
6. − x − 2 > 17 negative x minus , 2 greater than 17
7. − 4 z − 10 < − 12 negative 4 z minus , 10 less than , minus 12
8. 9 x − 8 ≥ 82 9 x minus , 8 greater than or equal to 82
9. 6 n + 3 ≤ − 18 6 n plus . 3 less than or equal to , minus 18
10. c + 13 > 34 c plus . 13 greater than 34
11. 3 x − 5 x + 2 < 12 3 x minus , 5 x plus . 2 less than 12
12. 2 ( y − 5 ) > − 24 2 open y minus 5 close greater than negative 24
13. − 3 ( 4 x − 1 ) ≥ 15 negative 3 open 4 x minus 1 close , greater than or equal to 15
14. − n − 27 ≤ 92 negative n minus , 27 less than or equal to 92
15. 8 x − 4 + x > − 76 8 x minus , 4 plus , x greater than , minus 76
16. 8 y − 4 y + 11 ≤ − 33 8 y minus , 4 y plus . 11 less than or equal to , minus 33
17. x + 78 ≥ − 284 x plus , 78 greater than or equal to , minus 284
18. 4 ( 5 a + 3 ) < − 8 4 open 5 eh plus 3 close less than . minus 8

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