Writing and Solving Inequalities

2x + 8 ≤ 30

• x ≥ 11

• x ≤ 19

• x ≤ 11

• x < 19

12 > 2x + 8

• x > 2

• x < 2

• x > 4

• x < 4

2x + 3x ≥ 25

• x > 5

• x ≤ 5

• x ≥ 5

• x < 5

x/2 + 10 < 25

• x < 70

• x < 30

• x ≤ 70

• x ≤ 30

5x + 5 ≤ 50

• x ≤ 9

• x ≥ 11

• x < 9

• x ≤ 11

The table shows the cost per month of two cell phone plans. Which inequality can help determine how many phone calls you need to make per month so that Plan 2 is a better option?

• 25 - 0.35n > 37 - 0.25n

• 0.35n + 25 > 0.25n + 37

• 25 - 0.35n < 37 - 0.25n

• 0.35n + 25 < 0.25n + 37

A local bakery has a daily operating cost of $1800 plus a cost of $10 per cake they make. If a cake sells for $15, which equation could be used to determine the minimum number of cakes, c, they must sell each day to earn a profit?

• 15c < 1800 + 10c

• 15c > 1800 + 10c

• 15c = 1800 + 10c

• 10c < 1800 + 15c

At the beginning of the year, Ethan has $800 in his savings account and Faith has $1,280 in her savings account.  Each month, Ethan deposits and additional $25 in his account, while Faith withdraws $15 from her account.  Write an equation to show after how many months will Ethan’s account have a greater balance than Faith’s account?

• 800 - 25x  < 1280 - 15x

• 800 + 25x < 1280 - 15x

• 800 + 25x  > 1280 - 15x

• 800 + 25x >  1280 + 15x

Sue's lunch account has $25 and she spends $2.50 every day. Troy's lunch account has $50 and she spends $3.25 every day. Write an inequality that shows when Sue's account will be more than Troy's.

• 25 - 2.5d > 50 - 3.25d

• 25 - 2.5d < 50 - 3.25d

• 25 + 2.5d > 50 + 3.25d

• 25 + 2.5d < 50 + 3.25d

Veronica is ordering trophies for her school. Company P charges $3.50 for each trophy and a one-time engraving fee of $25. Company R charges $7.50 for each trophy and a one-time engraving fee of $17. Which inequality can be used to find x, the minimum number of trophies that can be ordered so that the total charge at company P is less than the total charge at Company R?

• 3.5 + 25x < 7.5 + 17x

• 3.5 + 25x > 7.5 + 17x

• 3.5x + 25 < 7.5x + 17

• 3.5x + 25 > 7.5x + 17