5.1 Solving Inequalities by Addition and Subtraction

Objective: Solve Linear inequalities by using addition and subtraction

Graphing Inequalities

• < or > means open circle or means closed circle

Set-Builder Notation

Definition- A more concise way of writing a solution set.

The solution set for Example 1 is

20| xxThis is read the set of all numbers such that x is greater than or equal to 20.

Solve by adding or subtracting

812 x

Solve, Graph and Write the solution set.

822 m

Solve, Graph and Write the solution set.

c 207

Solve, Graph and Write the solution Set

aa 463

Solve, Graph and Write in set builder notation

1914 d

Solve, Graph and Write the answer in set-builder notation

nn 1019

Solve and Write the solution set

hh 4125

Phrases for Inequalities

< >

Less than

Fewer than

Greater Than

More Than

At most, no more than, less than or equal to

At least, no less than, greater than or equal to

Write and Graph the Inequality

a) You must be at least 16 years old to go on the trip.

b) The sum of a number and -4 is more than 8

c) Twice a number is less than the sum of that number and 9

d) The sum of twice a number and 5 is at most that number minus 3

Word Problem

Sanjay has $65 to spend at the mall. He bought a T-shirt for $18 and a belt for $14. If Sanjay still wants to buy a pair of jeans, how much can he spend?

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