Question

Solve each of the following equations by the trial-and-error method:
(i) y + 9 = 13
(ii) x − 7 = 10
(iii) 4x = 28
(iv) 3y = 36
(v) 11 + x = 19
(vi) $\frac{x}{3}=4$
(vii) 2x − 3 = 9
(viii) $\frac{1}{2}x+7=11$
(ix) 2y + 4 = 3y
(x) z − 3 = 2z − 5

Answer 1

(i) y + 9 = 13
We try several values of y until we get the L.H.S. equal to the R.H.S.

y	L.H.S.	R.H.S.	Is LHS =RHS ?
1	1 + 9 = 10	13	No
2	2 + 9 = 11	13	No
3	3 + 9 = 12	13	No
4	4 + 9 = 13	13	Yes

∴ y = 4

(ii) x − 7= 10
We try several values of x until we get the L.H.S. equal to the R.H.S.

x	L.H.S.	R.H.S.	Is L.H.S. = R.H.S.?
10	10 − 7 = 3	10	No
11	11 − 7 = 4	10	No
12	12 − 7 = 5	10	No
13	13 − 7 = 6	10	No
14	14 − 7 = 7	10	No
15	15 − 7 = 8	10	No
16	16 − 7 = 9	10	No
17	17 − 7 = 10	10	Yes

∴ x = 17

(iii) 4x = 28
We try several values of x until we get the L.H.S. equal to the R.H.S.

x	L.H.S.	R.H.S.	Is L.H.S. = R.H.S.?
1	4 $\times$ 1 = 4	28	No
2	4 $\times$ 2 = 8	28	No
3	4 $\times$ 3 = 12	28	No
4	4 $\times$ 4 = 16	28	No
5	4 $\times$ 5 = 20	28	No
6	4 $\times$ 6 = 24	28	No
7	4 $\times$ 7 = 28	28	Yes

∴ x = 7

(iv) 3y = 36
We try several values of x until we get the L.H.S. equal to the R.H.S.

y	L.H.S.	R.H.S.	Is L.H.S. = R.H.S.?
6	3 $\times$ 6 = 18	36	No
7	3 $\times$ 7 = 21	36	No
8	3 $\times$ 8 = 24	36	No
9	3 $\times$ 9 = 27	36	No
10	3 $\times$ 10 = 30	36	No
11	3 $\times$11 = 33	36	No
12	3 $\times$ 12 = 36	36	Yes

∴ y = 12

(v) 11 + x = 19
We try several values of x until we get the L.H.S. equal to the R.H.S.

x	L.H.S.	R.H.S.	Is L.H.S. = R.H.S.?
1	11 + 1 = 12	19	No
2	11 + 2 = 13	19	No
3	11 + 3 = 14	19	No
4	11 + 4 = 15	19	No
5	11 + 5 = 16	19	No
6	11 + 6 = 17	19	No
7	11 + 7 = 18	19	No
8	11 + 8 = 19	19	Yes

∴ x = 8

(vi) $\frac{x}{3}=4$
Since R.H.S. is an natural number so L.H.S. must also be a natural number. Thus, x has to be a multiple of 3.

x	L.H.S.	R.H.S.	Is L.H.S. = R.H.S.?
3	$\frac{3}{3}=1$	4	No
6	$\frac{6}{3}=2$	4	No
9	$\frac{9}{3}=3$	4	No
12	$\frac{12}{3}=4$	4	Yes

∴ x = 12

(vii) 2x − 3 = 9

We try several values of x until we get the L.H.S. equal to the R.H.S.

x	L.H.S.	R.H.S.	Is L.H.S. = R.H.S.?
1	2 $\times$ 1 − 3 = −1	9	No
2	2 $\times$ 2 − 3 = 1	9	No
3	2 $\times$ 3 − 3 = 3	9	No
4	2 $\times$ 4 − 3 = 5	9	No
5	2 $\times$ 5 − 3 = 7	9	No
6	2 $\times$ 6 − 3 = 9	9	Yes

∴ x = 6

(viii) $\frac{1}{2}x+7=11$
Since, R.H.S. is a natural number so L.H.S. must be a natural number Thus, we will try values if x which are multiples of 'x'

x	L.H.S.	R.H.S.	Is L.H.S. = R.H.S.?
2	2/2 + 7 = 8	11	No
4	4/2 + 7 = 9	11	No
6	6/2 + 7 = 10	11	No
8	8/2 + 7 = 11	11	Yes

∴ x = 8

(ix) 2y + 4 = 3y
We try several values of y until we get the L.H.S. equal to the R.H.S.

y	L.H.S.	R.H.S.	Is L.H.S. = R.H.S.?
1	2 $\times$ 1 + 4 = 6	3 $\times$ 1 = 3	No
2	2 $\times$ 2 + 4 = 8	3 $\times$ 2 = 6	No
3	2 $\times$ 3 + 4 = 10	3 $\times$ 3 = 9	No
4	2 $\times$ 4 + 4 = 12	3 $\times$ 4 = 12	Yes

∴ y = 4

(x) z − 3 = 2z − 5
We try several values of z till we get the L.H.S. equal to the R.H.S.

z	L.H.S.	R.H.S.	Is L.H.S. = R.H.S.?
1	1 − 3 = −2	2 $\times$ 1 − 5 = −3	No
2	2 − 3 = −1	2 $\times$ 2 − 5 = −1	Yes

∴ z = 2