This document discusses solving inequalities using addition and subtraction. It provides examples of writing inequalities from words and graphs, as well as solving inequalities algebraically. Specifically, it shows how to write an inequality describing a speed limit of 45 mph or a child needing to be taller than 40 inches. It also demonstrates how to write inequalities from graphs and solve examples algebraically such as 9 ≥ x + 7 and -2 < y + 15, graphing the solutions.

1. 4.1 Solving Inequalities using
Addition and Subtraction

2. Vocabulary:
• inequality: a mathematical sentence
formed by placing an inequality symbol
between two expressions.
• graph of an inequality: is the set of points
that represent all solutions of the
inequality.
• equivalent inequalities: inequalities that
have the same solution.

3. Graphing:
• x>1 greater than open dot
• x<1 less than open dot
• x ≤1 less than or equal solid dot
• x ≥ 1 greater than or equal
solid dot

4. Example 1:Write and graph an inequality
that describes the situation
1.)The speed limit on the road is 45 miles
per hour.
2.) A child must be taller than 40 inches to
get on Space Mountain.

5. Example 2 Write inequalities from graphs
Write an inequality represented by the graph.
a.
SOLUTION
The shading includes all numbers to the right of
(greater than) – 6.5.
ANSWER
An inequality represented by the graph is x > – 6.5.

6. Example 2 Write inequalities from graphs
Write an inequality represented by the graph.
b.
SOLUTION
The shading includes 4 and all numbers to the left of
(less than) 4.
ANSWER
An inequality represented by the graph is x ≤ 4.

7. Example 3 Solve an inequality using subtraction
Solve 9 ≥ x + 7. Graph your solution.
9 ≥ x +7 Write original inequality.
.

8. Example 3 continue
Solve the inequality. Graph your solution.
– 2 < y + 15

9. Try on your own!!
Solve the inequality. Graph your solution.
7. y + 5 > 6
ANSWER y >1
8. x + 7 ≥ – 4
ANSWER x ≥ –11