Signs and Symbols
Greater than
>
x > 3
open circle to the right
4x - 5 > 11
x > 4
Molly has completed 25 hours of community service. Her goal is to complete at least 90 hours this semester. Write and solve an inequality to show how many more hours Molly needs to complete to meet her goal.
x + 25 ≥ 90
x ≥ 65
When dividing by a negative you need to....
flip the symbol
Less than
<
x < -2
open circle to the left
x / 2 + 7 < 3
x < -8
Ella has $60 to spend at the state fair. If each ride costs $3, write and solve an inequality to represent that number of rides Ella can go on.
3x ≤ 60
x ≤ 20
Which are part of the solution set: x ≥ 2
x = 4
x = -5
x = 2.5
x = 0
4
2.5
greater than or equal to
≥
x ≤ 15
closed circle to the left
( x + 3 ) / 5 ≥ 2
x ≥ 7
The jazz band needs to raise at least $600 to travel to an upcoming competition. The members have already raised $350. Write and solve an inequality to represent the number of calendars they need to sell in order to afford the competition, if they make a $8 profit off each calendar.
350 + 8x ≥ 600
8x ≥ 250
x ≥ 31.25 OR 32 because we round up
when would we round down
When it comes to spending money with a limit
less than or equal to
≤
x ≥ 11
6 ( 2x+1) > 6
x > 0
A hot cup of coffee is 180OF. It loses heat at a rate of 4OF per minute. Write and solve an inequality to determine how long it will take for the coffee to be less than 140OF, which is the ideal drinking temperature according to experts.
180 - 4x ≤ 140
-4x ≤ -40
x ≥ 10
when would we round up
when needing to save money or raise money for something
Infinitely many solutions
3 ≥ x
closed circle to the left
4 (4 - x) ≤ -12
x ≥7
Mrs. Barns has $4,000 in savings at the beginning of the summer. She wants to have at least $800 in her account when she returns to work in September. Write and solve an inequality to figure out the maximum amount of money she can spend each week if summer break is 11 weeks long.
4000 - 11x ≥ 800
-11x ≥ -3200
x ≤ 290
round down
Will we ever use an equal sign when writing inequalities?
NO!