Page 119 - Start Up Mathematics_7

EXERCISE 7.3

1. Solve the following by method of transposition and verify your answers by substituting in
the equations:
5
(a) 3s + 12 = 0 (b) 3q – 5 = 7 (c) 8m – 3 = 13 (d) x = –5
2

(e) 17 + 3s = –4 (f) 0 = 16 + 4(m – 6) (g) 2x + 14 = 9x – 7 (h) 2(1 – x) = –12
2x 1 x 3 x + 1 x – 1
(i) 7(x – 2) – 4(5 – x) = 1 (j) – = + (k) =
3 3 2 2 3 2

2. Construct three linear equations starting with the given solution:
1 –1
(a) m = (b) n = –3 (c) q = –5 (d) x =
2 5

Applications of Linear Equations to Practical Situations

We have learnt how to convert daily life situations expressed in statement form to simple equations.
We also know how to solve linear equations to find the solution of practical problems and puzzles.
The steps to solve these word problems are as follows:
Step 1: Read the problem carefully.
Step 2: Figure out what we have to find and what is given.
Step 3: Assume the unknown quantity by variables x or y.

Step 4: Form an equation and solve it.
Step 5: Verify whether the solution satisfies the equation.

Example 15: Set up equations and solve them to find the unknown numbers in the following cases:
(a) Subtracting 6 from three times a number gives 9.
(b) One-fourth of a number minus 2 gives 3.
(c) If I take three-fourths of a number and count up 3 more, I get 21.
3
(d) Gaurav thinks of a number. If he takes away 5 from of the number, the result
2
11
is .
2

Solution: (a) Let the number be x. (b) Let the number be x.
Three times the number gives 3x One-fourth of a number minus 2
and on subtracting 6 from it we gives 3.
x
get 9. ∴ – 2 = 3
∴ 3x – 6 = 9 4 x
⇒ 3x = 9 + 6 ⇒ = 3 + 2
4
x
⇒ 3x = 15 ⇒ = 5
15 4
⇒ x = 3 ⇒ x = 20
⇒ x = 5

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