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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

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Mathematics: Pre Algebra

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