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For more information, please see full course syllabus of Pre Algebra
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Solving Inequalities by Adding or Subtracting

  • You can use inequalities to find minimum and maximum quantities that fit within parameters.
  • To solve an inequality, you can use the same process as solving an equation.
  • To solve an inequality, you can use reverse operations, such as the Addition Property of Equality and the Subtraction Property of Equality, to cancel operations and isolate the variable.

Solving Inequalities by Adding or Subtracting

x − 9 > 10. Solve for x.
  • x > 10 + 9
x > 19
5 + x < 3. Solve for x.
  • x < 3 − 5
x < − 2
9 ≤ x − 4.5. Solve for x.
  • 9 + 4.5 ≤ x
x ≥ 13.5
x − 2 ×5 − 13. Solve for x.
  • x − 10 ≥ − 13
  • x ≥ − 13 + 10
x ≥ − 3
9 < 18 − 3 + x. Solve for x.
  • 9 < 15 + x
  • 9 − 15 < x
x > − 6
− 11 + x ≤ 49 ÷7. Solve for x.
  • − 11 + x ≤ 7
  • x ≤ 7 + 11
x ≤ 18
| − 3 − 5|2 < x − 5. Solve for x.
  • | − 8|2 < x − 5
  • (8)2 < x − 5
  • 16 < x − 5
  • 16 + 5 < x
x > 21
An elevator can support at most 1200 pounds. If there are 500 pounds on the elevator, how many more pounds can the elevator support?
  • Let w = how much more weight the elevator can support.
  • 500 + w ≤ 1200
  • x ≤ 1200 − 500
x ≤ 700 pounds
You are trying to save at least $ 1000 for a vacation with your friends. So far, you have already saved $ 217.50. How much more money do you have to save?
  • $ 217.50 + m ≥ $ 1000
  • m ≥ $ 1000 − $ 217.50
m ≥ $ 782.50
There are 850 tickets available for a musical. So far, 320 tickets have been sold. Find how many more tickets can be sold.
  • 320 + t ≤ 850
  • t ≤ 850 − 320
t ≤ 530 tickets

*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 Inequalities by Adding or Subtracting

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.

  • Intro 0:00
  • What You'll Learn and Why 0:07
    • Topics Overview
  • Vocabulary 0:20
    • Addition Property of Equality
    • Subtraction Property of Equality
    • Example: x > 7
  • Solving an Inequality by Adding 1:33
    • Example: Solve x - 8 = 10
    • Example: Solve x - 8 < 10
  • Solving an Inequality by Adding 2:21
    • Example: 2 ≤ t - 5
    • Example: a - 8 > 15
  • Solving an Inequality by Subtracting 3:14
    • Example: How Many Students can Board the Bus?
  • Solving an Inequality by Subtracting 4:13
    • Example: How Many More Tickets can be Sold?
  • Extra Example 1: Solve the Inequality 5:16
  • Extra Example 2: Solve 8 ≥ 3 + m 5:52
  • Extra Example 3: MP3 Player 6:29
  • Extra Example 4: Write and Solve an Inequality 7:34