Download Lesson 4-4 Solving Two-Step Inequalities STUDY GUIDE Solve

Lesson 4-4
Solving Two-Step Inequalities
STUDY GUIDE
This study guide provides you with an overview of the types of problems and skills that we will learn or
have learned in the lessons listed above. In addition to this guide and the Lesson 4-1 to 4-3 study guide,
we will complete additional review problems in class, as we get closer to the test.
Solve each two-step inequality. Graph the solution.
1.) Solve 9 < 2(t + 5)
9 < 2(t + 5)
Write the inequality.
9 < 2t + 10
Use the Distributive Property.
9 < 2t + 10
Subtraction Property of Inequalities
-10
-10
–1 < 2t
Simplify.
–1 2t
2 <2
Division Property of Inequalities
1
1
– < t or t > –
2
2
Simplify.
Check by graphing the solution.
2.) Solve
𝒎
-2 >
-2 >
-2 >
–7
𝟔
𝑚
6
𝑚
6
–7
Write the inequality.
+ -7
Rewrite subtraction as addition.
7
6•5>
7
𝑚
6
t
•6
Addition Property of Inequality.
Multiplication Property of Inequality
30 > m or m < 30
Check by graphing the solution.
, m
-10x + 6x – 7 ≤ 9
3.) Solve
-10x + 6x – 7 ≤ 9
Write the inequality.
-10x + 6x + -7 ≤ 9
Rewrite subtraction as addition.
-4x + -7 ≤ 9
Combine like terms.
7
−4𝑥
−4
7
Addition Property of Inequality.
16
≤ −4
Division Property of Inequality
x ≥-4
Since you divided by a negative number,
reverse the inequality symbol.
Check by graphing the solution.
x
𝟒
4 > 8 – 𝟑𝒉
4.) Solve
4
4>8– ℎ
Write the inequality.
3
4
3
4 > 8 + −3ℎ
Rewrite subtraction as addition.
-8 -8
Subtraction Property of Inequality.
4
3
− 4 • -4 > − 3 ℎ • − 4
3 < h or h > 3
Check by graphing the solution.
Multiplication Property of Inequality
Since you multiplied by a negative number,
reverse the inequality symbol.
h