Solving Inequalities by adding Solving Inequalities by adding or subtracting, checking the or subtracting, checking the

inequality & graphing it!!inequality & graphing it!!

This is so easy you won’t even need one of these!!!

Solving the inequalitySolving the inequality

You are going to solve the inequality just You are going to solve the inequality just like you solve two step equations!!like you solve two step equations!!

Add or subtract a number from both sides Add or subtract a number from both sides of the inequality.of the inequality.

ExampleExample

1. n – 8 < 151. n – 8 < 15

+ 8 + 8+ 8 + 8 add 8 to both sides add 8 to both sides

n < 23 n < 23

2. -4 2. -4 ≥ a + 7≥ a + 7

-7 - 7 -7 - 7 subtract 7 from both sides subtract 7 from both sides

-11 -11 ≥ a≥ a

““Do we have to do the check?”Do we have to do the check?”

Let’s check the answers to our examples!Let’s check the answers to our examples!1.1. n – 8 < 15 n – 8 < 15 n < 23 n < 23 What are some possible solutions?What are some possible solutions? -Anything smaller than 23, let’s try 22!-Anything smaller than 23, let’s try 22!

n – 8 < 15n – 8 < 15 22 – 8 < 1522 – 8 < 15 14 < 15 14 < 15

ABSOLUTELY

““Do we have to do the check?”Do we have to do the check?”

Let’s check the answers to our examples!Let’s check the answers to our examples!2. -4 2. -4 ≥ a + 7≥ a + 7 -11 -11 ≥ a≥ a What are some possible solutions?What are some possible solutions? -Anything smaller than -11, let’s try -12!-Anything smaller than -11, let’s try -12!

-4 -4 ≥ a + 7≥ a + 7 -4 -4 ≥ -12 + 7≥ -12 + 7-4 -4 ≥ -5≥ -5

ABSOLUTELY

Then we have to graph it!Then we have to graph it!

Let’s graph the answers to our examples!Let’s graph the answers to our examples!

1. n – 8 < 15 1. n – 8 < 15 n < 23 n < 23

2. -4 2. -4 ≥ a + 7≥ a + 7 -11 -11 ≥ a≥ a

Your turn!! Your turn!! Solve it, check it, graph it (in this order).Solve it, check it, graph it (in this order).

1. w + 5 < 61. w + 5 < 6 2. x – 3 < 22. x – 3 < 2

3. -1 3. -1 ≤ y + 8≤ y + 8 4. z + 1 ≥ 64. z + 1 ≥ 6