5.5 Linear Inequalities A linear inequality describes the region of the coordinate 
plane that has a boundary line. Every point in the region 
is a solution. Solid lines – Each point on the line is a solution Dashed lines – Each point on the line is NOT a solution How did we represent x≥2 on a number line? How did we represent x>2 on a number line?

y x Graph y<2x+3 Solution: 1) In PENCIL graph y=2x+3 Ex. 1 Graph y<2x+3 Solution:  1) In PENCIL graph y=2x+3  2) Make the line dashed because of <  3) Test a point not on the line  4) Shade the region that makes the solution true y x 5 -5

Ex. 2 Solve 2x - 5y ≤ 10 y x 5 -5

y x y x Write an inequality to represent the graph below. TRY Ex. 3 -5

TRY Write the inequality for y x 5 -5

Ex. 4 Suppose you intend to spend no more than $12 on 
peanuts and cashews for a party. Peanuts cost $2 a 
pound and cashews cost $4 a pound. How many 
pounds of each can you buy?

TRY Suppose you are a coach and need to buy some balls for 
lacrosse and soccer. Your budget is no more than $90 on 
balls for both sports. Lacrosse balls cost $3 each and 
soccer balls cost $9 each. How many balls of each type 
can you buy?

y x Jack solved the following problem. Can you spot his mistake(s)? TRY Jack solved the following problem. Can you spot his 
mistake(s)?  y<x+4  0<0+4  0<4 - True y x 5 -5