Two-Step Inequalities
Solve the inequality
14-3g>32
g<-6
Solve!
-3<g-4<-1
1<g<3
Tim sold half of his comic books and then bought nine more. He now has less than eighteen. How many did he begin with?
Less than 18 Comic Books
When multiplying or dividing both sides of an inequality by a negative number, you:
Flip the direction of the inequality!
Solve and graph. -8(7x-7)>224
x<-3
w/4 -21>-3
w>72
Solve!
-4<f-5<-1
1<f<4
The quotient of x and 4 is at least the product of 2 and x.
Solve the inequalities. 5+m+8≥14 ; 13+n-26<38
m≥1 ; n<51
Solve and graph. 3m-8>-30+5m
m<11
4-3x<34
x>-10
Solve!
6+10x<76 or -3x-2<-14
All real numbers
Ida just lost her job. She has $1,540 in her bank account. If her expenses are $240 per week, how many weeks until she has less than $100 left in her bank account?
6 weeks
Solve: 3x+4<3x-6
No Solution
Solve and graph. 4(5-3b)>4b+4
b<1
(d+26)/5<3
d<-11
-10+3n>-19 or 8-6n<-28
n>-3
Three-fourths of a number minus 10 is at most twice that same number minus 5.
x is greater than or equal to -4.
A compound inequality with "or" means that when you graph, you are looking for the:
Union
Solve and graph. -(1+6k)>-1-6k
No Solution
-10x-6<6
x>0
5b-9<-9+4b<b-6
b<0
A car salesperson is paid a base salary of $45,000 a year plus 7% of sales. What are the sales needed to have an annual income greater than $85,000?
Sales need to be greater than $571,428
A compound inequality with "and" means that when you graph, you are looking for the:
Intersection
Solve and graph. 2(3x+2)+4(1-5x)>8
x<0