Page 162 - ICSE Math 7

AT A GLANCE

¾ An inequation is a statement which states that the two algebraic expressions are not
equal.

¾ An inequation in which the highest power of the variable is 1 is known as a linear
inequation.
¾ The set from which the values of the variable have to be selected to make an inequation true is
known as the replacement set or domain of the variable.
¾ The values of the variable from the replacement set which satisfy the inequation form the solution
set or truth set of the inequation.

MENTAL MATHS

Write the resulting inequation, when each side of the inequation:
(a) x > 6 is increased by 6 (b) x < –5 is increased by 9 (c) x > –7 is decreased by 7

–x –5 x
(d) x > –4 is increased by 4 (e) > is multiplied by 12 (f) > –3 is multiplied by –2
2 6 4
–x
(g) 4x > –32 is divided by 8 (h) < –20 is divided by –5
5

PRACTICE TIME

1. Solve the following inequations.
(a) 4(x – 1) > 2(x – 5), x ∈ W (b) 7x + 10 ≤ 8x – 9, x ∈ N
x
1
(c) 3x + 5 ≥ – 11, x ∈ Z (d) 2x – 3 < x – , x ∈ {1, 2, 3, 4, 5}
3
4
2. For the inequation –4 ≤ x < 2, draw separate number lines when:
(a) x ∈ N (b) x ∈ W (c) x ∈ Z
3. Solve the following inequations for x ∈ Z.
(a) 6x + 3 < 4x + 7 (b) 3(x – 1) ≤ 2(x – 3)
x x
(c) 6(x – 2) > 2(2x + 3) –10 (d) > + 1
2 3
(e) 8x – 7 > 5x – 1 (f) 9x – 8(x –3) < 37 – (3x + 5)
4. Rishi goes to a shopping mall. He decides not to spend more than ` 3,500. He buys a shirt for
` 800. How many pairs of shoes can he buy if each pair costs ` 900?

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