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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 7 - Mathematics
6.34 Properties of Inequalities - V

Examples:
  1. Consider the inequality 6 < 8.
    Take the reciprocals of numbers on both sides.
    Reciprocal of L.H.S = 1/6
    Reciprocal of R.H.S = 1/8
    Since 6<8 , 8 lies to the right of 6.
    Take their reciprocals, 1/6 and 1/8.
    1/6 is lies to the right of 1/8
    \ 1/6 > 1/8
    That is if 6 < 8 then 1/6 > 1/8.

  2. Consider the inequality -6 > -8.
    Take the reciprocals of numbers on both sides,
    Reciprocal of L.H.S. = -1/6
    Reciprocal of R.H.S. = -1/8
    -1/6 lies to the left of -1/8.
    \ -1/6 < -1/8.
    That is, if -6 > -8, then -1/6 < -1/8
If a and b are the same sign and a < b (a > b) then 1/a > 1/b (1/a < 1/b).
If reciprocals are taken to quantities of the same sign on both sides of an inequality then the order of the inequality is changed.

Example:
12 - 8x < - 3x + 20
Adding 3x both sides
12 - 8x + 3x < - 3x + 3x + 20
12 - 5x < 20
Subtracting 12 both sides
12 - 12 - 5x < 20 - 12
- 5x < 8
Dividing both sides by -5 reverses the inequality
x > -8/5


Directions: Write at least ten examples of your own and prove the above inequality property.
Q 1: 6x - 16 > 8x - 24
x > 4
x < -4
x < 4

Q 2: 15 - 6y > -5y + 16
y > -1
y < -1
y < 1

Q 3: 12 - 4a > -2a +24
a > -6
a < 6
a < -6

Q 4: 10 - 7x > -5x + 15
x > 5/2
x > -5/2
x < -5/2

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Question 6: This question is available to subscribers only!


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