1. Solvig Inequalities

2. What rules apply to solving inequalities?
7 > 5
5 > 3
2 ∙ ∙ 2
10 > 6
5 > 3
– – 2
3 > 1
5 >3
– 2 ∙ ∙ – 2
– 10 > – 6
– 10 < – 6
5 > 3

3. Solve given inequalities. Show all steps.
a) -2 ≥ 8 + m b) v – 5 < 12
–8 –8
–10 ≥ m
v < 17

4. Solve given inequalities. Show all steps. c) 𝑔 2 > 7 d) 5n ≤ 52
2∙ ∙2
g > 14
5n ≤ 25
n ≤ 5

5. Example:
It costs a bakery company $72 to make cakes. How many cakes must it sell at $12 apiece to make a profit? Write an inequality with a variable for the unknown to represent the situation and solve.

6. 12c > 72 12 12 c > 6 or c ≥ 7 c = number of cakes sold
It costs a bakery company $72 to make cakes. How many cakes must it sell at $12 apiece to make a profit? Write an inequality with a variable for the unknown to represent the situation and solve.
c = number of cakes sold
To earn profit Income > Expenses
12c > 72
c > 6
or c ≥ 7
The bakery must sell more than 6 cakes or at least 7 cakes to make a profit.

7. Solve given inequality. Show all steps.
a) 2x + 3 > –12
– – 3
2x > –15 2
x > –7.5

8. Solve given inequality. Show all steps. b) –3x + 5 < 23
Do not forget, when multiplying or dividing both sides of an inequality by a negative number, we need to switch the inequality sign.
– – 5
– 3x < 18
–3 –3
x > – 6

9. Example:
A phone company charges $29 per month and $0.02 per minute of long distance. If you want to spend no more than $40 per month on the phone calls, how many minutes can you use? Write an inequality with a variable for the unknown to represent the situation and solve.

10. A phone company charges $29 per month and $0
A phone company charges $29 per month and $0.02 per minute of long distance. If you want to spend no more than $40 per month on the phone calls, how many minutes can you use? Write an inequality with a variable for the unknown to represent the situation and solve.
m = # of minutes What you spend ≤𝟒𝟎
m ≤ 40
– –29
0.02m ≤11
m ≤ 550