Page 52 - Maths Skills - 7

50 Maths

(vii) 2x + 14 = 9x – 7 (viii) 2 (l – x) = – 12 (ix) 7 (x – 2) – 4(5 – x) = 1
2x 1 x 3 x + 1 x – 1 x 3 x x
(x) – = + (xi) = (xii) + = +
3 3 2 2 3 2 2 4 4 6

2. Solve the equations and verify your results.
7
2
(i) 5x – 6 = 9 (ii) – 6 (x + 7) = 6 (iii) x = 17 (iv) x = 15
9
9
x 8 1
(v) 6 + 3 (x – 3) = 16 (vi) + 1 = 19 (vii) x = 2x – (viii) 2y – = 17
3 5 2
(ix) 4 (3x + 2) – 5 (6x – 1) = 2 (x – 8) + 4x (x) 20x + 35 = 27x – 18
APPLICATIONS OF SIMPLE EQUATIONS
Simple equations can be used to solve daily life situation. We convert the word problem into mathematical equation
and then solve. This can be illustrated more clearly with few examples given below.

Let’s Attempt

Example 1: Add 4 to eight times a number to get 60. Example 2: Farhan subtracts thrice the number of
Solution: Let the number be x. notebooks he has from 50. He finds the

8 times the number is 8x. Solution: result to be 8.
Let x be the number of notebooks
Adding 4 to 8 times the number will Farhan has, then 3x subtracted from 50
become 8x + 4 gives
But, this sum is equal to 60. 50 – 3x = 8
Thus 8x + 4 = 60 – 3x = 8 – 50

8x = 60 – 4 or – 3x = – 42
8x = 56 On dividing both the sides by – 3, we
On dividing both the sides by 8, we get get
8x = 56 – 3x = – 42
– 3
– 3
8 8 or x = 14
x = 7
Thus, Farhan has 14 notebooks.

Example 3: Vidisha thinks of a number. If she adds Example 4: Anwar thinks of a number. If he takes
19 to it and divides the sum by 5, she away 7 from 5 of the number, the
will get 8. Find the number. 11 2
Solution: Let the number be x. result is 2 . Find the number.
Solution: Let the number Anwar thinks be x.
(x + 19) ÷ 5 = 8 5 11
Then, x – 7 =
x + 19 2 2
or = 8
5 5 11
Multiplying both the sides by 5, or 2 x = 2 + 7

(x + 19) × 5 = 8 × 5 5 x = 11 + 14
5 2 2
x + 19 = 40 or 5 x = 25

x = 40 – 19 2 2
x = 21