Solvig Inequalities

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

Solve given inequalities. Show all steps. a) -2 ≥ 8 + m b) v – 5 < 12   –8 –8 –10 ≥ m +5 +5 v < 17 -12 -11 -10 -9 -8 15 16 17 18 19

Solve given inequalities. Show all steps. c) 𝑔 2 > 7 d) 5n ≤ 52 2∙ ∙2 g > 14 5n ≤ 25 5 5 n ≤ 5 12 13 14 15 16 3 4 5 6 7

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.

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 12 12 c > 6 or c ≥ 7 The bakery must sell more than 6 cakes or at least 7 cakes to make a profit.

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

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 – 5 – 3x < 18 –3 –3 x > – 6

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.

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 29 + 0.02m ≤ 40 –29 –29 0.02m ≤11 0.02 0.02 m ≤ 550