Middle School Graphing Inequalities

An elevator can only hold 1500 pounds. If equipment weighs 945 pounds, how much more pounds of supplies can be put on the elevator? Which inequality would represent this situation?  

• x - 945 > 1500

• x + 945 > 1500

• x - 945 ≤ 1500

• x + 945 ≤ 1500

Which word problem represents the inequality:
x + 32 ≥ 80
(Show work by writing down inequality clue words.)

• Janine's goal is to earn at least $80 for soccer camp.  She has earned $32 so far.  How much more does she need to earn?

• Janine made more than 80 points during the basketball season.  She made 32 points the first five games.  How much did she score the rest of the games?

• Janine scored above an 80 on her math homework.  But, she turned her work in late and was deducted 32 points.  What did she make after the deduction?

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

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

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

8x < 48

• x < -6

• x > -6

• x < 6

• x > 6

Answer explanation

To solve 8x < 48, divide both sides by 8: x < 6. Thus, the correct answer is x < 6.

10 ≥ x - 3

• x ≤ 13

• x ≥ 13

• x ≤ 7

• x ≥ 7

Answer explanation

To solve 10 ≥ x - 3, add 3 to both sides: 13 ≥ x. This can be rewritten as x ≤ 13, which matches the correct answer choice.

-4 + y < -8

• y < 4

• y < -12

• y < -4

• y < 12

Answer explanation

To solve -4 + y < -8, add 4 to both sides: y < -4. Thus, the correct answer is y < -4.

Solve.

• z≤1

• z>9

• z≤9

• z<9

Answer explanation

To solve the inequality, we find that z can take any value less than or equal to 9. Thus, the correct choice is z≤9, as it includes all values up to 9, while the other options do not satisfy this condition.

• x > 12

• x < 24

• x = 12

• x < 12

Answer explanation

To solve the inequality 12 + x > 24, subtract 12 from both sides: x > 12. Thus, the correct answer is x > 12.