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Solving Two-Step Inequalities

  • A two-step inequality is an inequality that contains two operations such as addition and division or subtraction and multiplication.
  • Solving two-step inequalities is very similar to solving two-step equations. Use inverse operations to isolate the variable. A difference is that in inequalities, when multiplying or dividing each side by a negative number, the inequality sign must be reversed.

− 2x + 7 ≤ − 15. Solve for x.

  • − 2x ≤ − 15 − 7
  • − 2x ≤ − 22
  • x ≤ − 22 ÷( − 2)

x ≥ 11

[x/5] + 11 < 27. Solve for x.

  • [x/5] < 27 − 11
  • [x/5] < 16
  • x < 16 ×5

x < 80

− 8x + 2 > 66. Solve for x.

  • − 8x > 66 − 2
  • − 8x > 64
  • x < 64 ÷− 8

x < − 8

− 2(9 + x) ≤ 24. Solve for x.

  • 9 + x ≥ 24 ÷( − 2)
  • 9 + x ≥ − 12
  • x ≥ − 12 − 9

x ≥ − 21

[x/( − 0.1)] + 4 > 11. Solve for x.

  • [x/( − 0.1)] > 11 − 4
  • [x/( − 0.1)] > 7
  • x < 7 ×( − 0.1)

x < − 0.7

9 − [x/4] < 49. Solve for x.

  • − [x/4] < 49 − 9
  • − [x/4] < 40
  • x > 40 ×− 4

x > − 160

25x − 40 ≥ 10. Solve for x.

  • 25x ≥ 10 + 40
  • 25x ≥ 50

x ≥ 2

9 − 7x < 5. Solve for x.

  • − 7x < 5 − 9
  • − 7x < − 4
  • x > − 4 ÷( − 7)

x > [4/7]

Emily has $ 55 to spend at the mall. She buys a pair of jeans for $ 26 and sunglasses for $ 15. Emily decides to spend the rest of her money on soft pretzels, which cost $ 1.50 each. At most, how many pretzels can Emily buy?

  • Let x = number of soft pretzels Emily can buy.
  • $ 26 + $ 15 + $ 1.50x ≤ $ 55
  • $ 41 + $ 1.50x ≤ $ 55
  • $ 1.50x ≤ $ 55 − $ 41
  • $ 1.50x ≤ $ 14
  • x ≤ 9.3

Emily can buy 9 pretzels at most

Daniel has $ 23 to spend on school supplies. He needs to buy a book for English class and notebooks. The textbook costs $ 18.75, and one notebook costs $ 1.60. How many notebooks can Daniel buy?

  • Let n = number of notebooks Daniel can buy.
  • $ 18.75 + $ 1.60n ≤ $ 23
  • $ 1.60n ≤ $ 23 − $ 18.75
  • $ 1.60n ≤ $ 4.25
  • n ≤ 2.66

Daniel can buy 2 notebooks at most.

0.6 − 2.8x ≤ 9[2/5]. Solve for x.

  • − 2.8x ≤ 9[2/5] − 0.6
  • − 2.8x ≤ [29/5] − [6/10]
  • − 2.8x ≤ [29/5] − [3/5]
  • − 2.8x ≤ [26/5]
  • x ≥ [26/5] ×( − 2.8)
  • x ≥ [26/5] ×( − 2[8/10])
  • x ≥ [26/5] ×( − [28/10])
  • x ≥ [26/5] ×( − [14/5])
  • x ≥ − [364/25]

x ≥ − 14.56

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Solving Two-Step Inequalities

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Mathematics: Pre Algebra