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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 7 - Mathematics
6.31 Properties of Inequalities - II

Examples:
  1. Consider the inequality 14 < 16
    Multiplying both sides by 2m we get,
    L.H.S. = 14 * 2 = 28
    R.H.S. = 16 * 2 = 32
    Since 14 < 16, 16 lies to right of 14.
    After multiplying both sides by 2.
    16 * 2 = 32 lies the right of 14 * 2 = 28.
    \ 28 < 32
    i.e., If 14 < 16 then 14* 2 < 16 * 2.

  2. Consider the inequality 14 > 10
    Multiplying both sides by 1/2, we get
    L.H.S. = 14 * 1/2 = 7
    R.H.S. = 10 * 1/2 = 5
    Since 14 > 10, 14 lies to the right of 10.
    After multiplying both sides of the inequality by 1/2,
    14 * 1/2 = 7 lies the right of 10 * 1/2 = 5
    \ 7 > 5.
    i.e., If 14 > 10 then 14 * 1/2 > 10 * 1/2.

    Multiplying (or dividing) both sides of a inequality by the same positive number does not change the order of the inequality sign.
    For any three numbers a,b,c where c > 0.
    (1). If a < b, then ac < bc and a/c < b/c.
    (2). If a>b, then ac > bc and a/c > b/c.


Example 1: Solve for x in the inequality
4x - 3 < x + 1
Adding 3 to both sides of the inequality
4x - 3 + 3 < x + 1 + 3
4x < x + 4
3x < 4 ---- dividing both sides of a inequality by 3 does not change the order of the inequality sign.
x < 4/3

Example 2: Solve for x in the inequality
x/4 < 4 ---- multiplying both sides of a inequality by 4 does not change the order of the inequality sign.
x < 16


Directions: Solve for the variable in the inequalities given below. Write at least ten examples of your own and prove the above inequality property.
Q 1: 9x < -81
x > -9
x < -9
x < 9

Q 2: x/12 < 2
x < 24
x > 24
x < -24

Q 3: 10x < -340
x > -34
x < -34
x < 34

Q 4: x/3 > 5
x < 15
x > -15
x > 15

Q 5: r/3 > 9
r > 27
r < 27
r > -27

Q 6: x/8 > 9
x < 72
x > -72
x > 72

Q 7: x/6 > 7
x < 42
x > 13
x > 42

Q 8: 5x < -25
x > -5
x < 5
x < -5

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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