Name:_______________________________ EXPRESSING THE SOLUTION TO INEQUALITIES
Solve the following inequality:
Math 8 (4.1) Solve and Graph Inequalities SOL 8.15 (b) 3 x  2  11
There are three ways to express the solution to this inequality.
1) On a GRAPH:
2) INTERVAL notation:
3) SET notation:
DIVIDING AN INEQUALITY BY A NEGATIVE
When dividing both sides of an inequality by a negative number, remember this causes
the inequality symbol to reverse direction!
Examples:
a) 3 y  48
b)
5 y  2   17
You try…..solve each inequality below.
Express your solution as interval notation, on a graph, and as set notation.
1)
3y  2  8
2)
3)
26  2 x  40
4)
2
 x  5  3
8
3 x  8  28  7 x
Math 8
Practice 4.2 Solve Two-Step Inequalities
Name ________________________
Date: _____________ Block: ____
DO NOT forget to reverse the inequality symbol whenever YOU multiply or divide both sides by a
negative number.
Solve the inequality. Graph your solution.
1. 4x – 7 ≥ 1
3(a – 4) ≤ 33
4.
7. –y + 2 <
2. 11 <
5.
8.
+3
(y + 1) > 6
– 6 ≤ 3
3. 11 <
6.
9. 7 –
+3
(c – 1) < –22
< 4
–5m – < 4 10.
11. 1.7 – 11d > –6 12. –(2 + n)  –30
14. 8 – 2n ≥ 8 15. 3b + < 13. –8y > –2y + 24 For the given value, state whether the inequality is true or false.
16. –p + 7 ≥ 6, p = –2 17. n – 2 ≥ 2, n = 7 18. –3b + 1 < –11, b = 4
19. 5.1 < 3(0.7h + 0.1), h = 2 20. 4.5 
21. 2c + 11 > 19 c = 4 + 2, x = 3 Evaluate each expression if a = 5 and b = –2.4. Write < , > or = in the blank.
22. 8b – 5a ____ –2b 23. _____ –b Translate the verbal phrase into an inequality. Then solve the inequality and graph your
solution.
25.
Six and 3 tenths less than 5 times a number x is
greater than or equal to eight and seven tenths.
26. The difference of 4 and twice the x is less than 8.
28. Complete the chart.
Inequality
n ≥ 3 Graph
Three solutions to the inequality
4 ‐1 < y ‐3 x ≤ 4.5