Graph Inequalities
Graph the inequality problem!
n <= -5
<----------@
---|------------|---
-6 -5
Write the inequality for the graph!
@--->
----|----
6
x >= 6
Write an inequality to represent the situation!
The minimum wage in Idaho was $7.25 in 2020.
x >= 7.25
Solve the inequality.
x/6 > -5 OR -7x - 2 <= 12
Write an inequality, define all variable, solve the inequality, and interpret the solution.
A canoe rental shop rents canoes for $20 plus $35 per hour. You do not want to spend more than $230.
230 >= 35x + 20
m = 35, b = 20, x = # of hours rented, y = total cost
x <= 6
You must rent for 6 or less hours to not spend more than $230!
Graph the inequality below!
x <= 5 AND x > -2
O--------------@
---|-------|-------|--
-2 3 5
Write the inequality for the graph!
<- -@
---------|-----
12
x <= 12
Write an inequality to represent the situation.
The maximum speed limit on HWY 52 is 65 mph.
x <= 65
Solve the inequality.
7x + 13 < 4x + 1
x < -4
Write an inequality, define all variable, solve the inequality, and interpret the solution.
Charlie is saving $5 per week and already has $15 saved. He wants to save at least $75.
75 <= 5x + 15
m = 5, b = 15, x = # of weeks, y = total $ saved
x >= 12
Charlie must save for 12 or more weeks to save $75!
Graph the inequality below!
x > 3 OR x <= -1
<-@ O--->
---|-------|-------|-----
-1 1 3
Write the inequality for the graph!
@------@
-----|-------|----
1 7
1 <= x <= 7
Write an inequality to represent the situation.
Park visitors can get a free pass if they are 3 years old and under or if they are 65 years old and older.
x <= 3 OR x >= 65
Solve the inequality!
-10 <= 2x - 1 < -4
-9/2 <= x < -3/2
Write an inequality, define all variable, solve the inequality, and interpret the solution.
On a field trip, 20 students rode in cars and the rest filled 5 buses. No more than 250 students went on the trip.
250 >= 5x + 20
m = 5, b = 20, x = # of students on 1 bus, y = total students
x<= 45
Each bus must have had 45 or less students on it!
Graph the inequality below!
x > 3 AND x > 5
O--->
---|-------|-------|-----
3 4 5
Write the inequality for the graph!
<--O O--->
---|-------|---
-6 8
x < -6 OR x > 8
Write an inequality to represent the situation.
The optimal body temperature for an adult is between 96 and 102 degrees.
96<x<102
Solve the inequality.
-3(x - 4) - 1 >= 2x - 6x - 7
x >= -18
Write an inequality, define all variable, solve the inequality, and interpret the solution.
Amanda rents a bike for $2 per hour plus a one time fee of $10. she paid a total of less than $28.
28 > 2x + 10
m=2, b=10, x=#hours, y=total cost
x < 9
She must have rented the bike for less than 9 hours!
Graph the inequality below!
x >= 2 OR x > 6
@------------------>
---|-------|-------|-----
2 4 6
Write the inequality for the graph!
<-O @---->
---|-------|------
5 6
x < 5 OR x >= 6
Write an inequality to represent the situation.
Anna is trying to figure out how old someone is. She knows that this person is either older than 1.5 times her age or less than half her age. She is 24.
x >= 36 OR x <= 12
Solve the inequality below.
-6(1 + 7k) + 7(1 + 6k) <= -2
1 <= -2
FALSE! No Solution!
Write an inequality, define all variable, solve the inequality, and interpret the solution.
Eliza won 40 pieces of candy. She shared 2 pieces with each of her friends but still has at least 6 pieces left.
6 <= 40 - 2x
m = -2, b = 40, x = # of friends, y = pieces left
x <= 18
She must have 18 or less friends!