Page 175 - ICSE Math 8

3. Solve the following inequations.
(a) 2x > x + 8, x ∈ {7, 8, 9, 10, 11} (b) 2(x + 8) ≥ x – 15(x – 3), x ∈ {–1, 0, 1, 2, 3}
x x
(c) 3(2x – 3) ≤ 5 – 2(x + 3), x ∈ W (d) 2 – 2 ≥ + 1, x ∈ Z
3
x 3x
(e) 5 – < – 6, x ∈ N
3 2
4. Find the solution set and represent it graphically.
(a) 4 < 2x – 3 ≤ 5, x ∈ W (b) 12 ≥ x + 8 ≥ 10, x ∈ N
(c) 15 > 4 + 2x ≥ 6, x ∈ N (d) –5 < 3x – 2 ≤ 10 – x, x ∈ W
(e) 3 < 11 – 3x ≤ 9, x ∈ W

AT A GLANCE

¾ An equation consisting of only one variable is called a linear equation in one variable.
¾ The solution or root of a linear equation is the value of the variable which satisfies the equation.
¾ Same number can be added to or subtracted from both the sides of an equation without affecting the
equality.

¾ Both sides of an equation can be multiplied or divided by the same number ‘m’ (m ≠ 0) without affecting the
equality.
¾ Any term of the equation can be transposed to the other side by changing its sign.
¾ An inequation is an algebraic statement which states the inequality two algebraic expressions.
¾ An inequation in which the highest power of the variable is one 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 set of values of the variable from the replacement set which when substituted makes the inequation
true is known as the solution set or truth set.

MENTAL MATHS

1. Choose the correct option.
(a) The linear equation that represents the statement “4 times the number of coins in my pocket plus
5 more is 29” is:
(i) 4x – 5 = 29 (ii) 4x + 29 = 5 (iii) 4x + 5 = 29 (iv) None of these
1
(b) The value of x in the equation = 5 is:
x + 1
−4 4 5 −5
(i) (ii) (iii) (iv)
5 5 4 4
x − 2 a
(c) The solution of the equation, = 0 is:
2
(i) x = 2a – 2 (ii) x = 2a (iii) x = 2a + 2 (iv) x = – 2a

(d) If 5(x – 3) – 4(x – 2) = 0, the value of x is:
(i) 8 (ii) –7 (iii) –8 (iv) 7
(e) While solving an equation the same number or expression can be:
(i) added or subtracted on both sides (ii) multiplied on both sides
(iii) divided, if non-zero on both sides (iv) all of these

163