Two-step inequalities
3 + 4x > 27
x > 6
The maximum number of students in a classroom is 26. If there are 16 students signed up for the art class, how many more can join?
x + 16 </ (less than or equal to) 26
x + 5 < 17
x < 12
Solve for L
A = LW
L = A/W
2(n + 3) - 4 < 6
n < 2
50 - 8t < 90
t > -5
Juan is raising money for a local charity by washing cars. He is charging $15 per car wash. He spent $27 on supplies. He wants to raise at least $100 for the charity. Write an inequality to represent this situation.
15x - 27 </ 100
x - 4 > 12
x >16
Solve for x:
(x + 2) / 3 = 5
x = 13
19 - 2(1 - x) < 13
3.5 + 4t < 39.5
t < 9
Daniel's neighbor paid him to take care of their dog when they went on vacation. He earned $12.00 a day. He spent $13 of his earnings on a book and art supplies. After his spending, he had more than $40 left. How much could Daniel's neighbors have paid him?
12x - 13 > 40
14 < 2x
x > 7
Solve for z:
c = a + z
z = c - a
-2(z + 5) + 20 > 6
z < 2
8 - n/4 > 20
n < -48
Ryan is a wrestler trying to make weight. He currently weighs 200lbs. If he cuts 2 lbs. per week, how many weeks will it take him to weigh less than 175 lbs?
Write an inequality to represent this.
200 - 2x < 175
x /10 > 2.5
x > 25
Solve for x:
y = mx + b
x = (y - b) / m
4(1.1z + 2.75) > -6.6
z > -4
-3x - 24 < -36
x > 4
Sarah rented a bike from Shawna's Bikes. They charged her $2 per hour, plus a 10 fee. Sarah paid less than $29.
Write an inequality to represent this.
10 + 2x < 29
x/-4 < 5
x > -20
When do you flip the symbol of an inequality when solving?
Multiplying or Dividing by a negative number
24 > 58 + 5(x - 3.8)
x < -3