Page 152 - ICSE Math 7

EXERCISE 13.2

1. Solve the following equations by trial and error method.

(a) 2p – 3 = 15 (b) 3x + 14 = 14 (c) 5p – 16 = 69 (d) 6m + 13 = 1
2. Write the step you will use to separate the variable and then solve the equation.

(a) y + 4 = 6 (b) x + 5 = 8 (c) x – 6 = 13 (d) x = 8
2
3. Mention the steps you will use to separate the variable and then solve the equation.

1
(a) 2(x – 1) = 10 (b) 5x – 25 = 0 (c) x + = 1 (d) –2 – x = 6
2 2
4. Solve the following equations.
1
(a) 3y = 12 (b) x – 5 = 1 (c) x + 2 = 11 (d) 2x – = 1
4 5 7 4

Transposing a Term of an Equation

In an equation a term can be shifted from one side to the other side by changing its sign. This process
is known as transposition. A positive term changes to negative and a negative term changes to positive
on transposition. Transposing a number is equivalent to adding (or subtracting) the same number to
both sides. Hence it does not affect the equation in any way.

Example 6: Solve the following equations.
7
(a) 3y + = 43 (b) q + 7 = 7
3 3 4

7 43 q
Solution: (a) 3y + = (b) + 7 = 7
3 3 4
q
⇒ 3y = 43 – 7 ⇒ = 7 – 7
3 3 4

q
⇒ 3y = 43 – 7 ⇒ = 0
3 4

⇒ 3y = 36 ⇒ q = 0
3
⇒ 3y = 12
⇒ y = 4

Example 7: Construct two linear equations starting with x = –2.
Solution: (i) x = –2 (ii) x = –2

x –2
⇒ 2x = 2 × –2 ⇒ =
2 2
x
⇒ 2x = –4 ⇒ = – 1
2
x
⇒ 2x + 4 = –4 + 4 ⇒ + 1 = 0
2
⇒ 2x + 4 = 0

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