Page 150 - ICSE Math 6

–3
Verification: Substitute x = in LHS
2

4(x + 2) = 4   –3 +2 =    4  –3+ 4   = 4   1   = 2
 2   2   2 
–3
Substitute x = in RHS
2
 –3 
2x + 5 = 2   + 5 = –3 + 5 = 2
 2 

As LHS = RHS, therefore the solution x = –3 is correct.
2
y 1
(c) +1 2=
7 7
y 15
⇒ +1=
7 7
⇒ y = 15 − 1 (Transposing 1 to the other side)
7 7
y 15 7− 8
⇒ = =
7 7 7
y 8
⇒ × 7 = × 7 (Multiplying both sides by 7)
7 7
⇒ y = 8

Verification: Substitute y = 8 in LHS
y 8 8 + 7 15 1
+ 1 = +1= = = 2 = RHS
7 7 7 7 7
As LHS = RHS, therefore the solution y = 8 is correct.

EXERCISE 13.1

1. Express each of the following statements in algebraic form.
(a) A number when increased by 21 gives 30.
(b) Twice of a number when decreased by 9 gives 11.
(c) x subtracted from 10 equals 3.
(d) 18 divided by x is equal to 6.
(e) One-fourth of a number when added to two-sevenths of the same number gives 135.
(f) The sum of two consecutive numbers is 21.
2. Write suitable statements for the following algebraic expressions.

(a) 15 – x = 6 (b) 4x – 4 = 76 (c) a + 3 = 5 (d) 3a + 9 = 15
10
(e) 7 – a = 2 (f) x = 1 (g) y + 5 = 10 (h) 3z – 10 = 2
3. Solve.
x 1
(a) 2a + 6 = 8 (b) x – 3 = 15 (c) +2 3=
7 2
y x 5z
(d) +5 5= (e) 10 − = 30 (f) = 10
5 3 20

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