Simple Linear Equations — Exercise 14(A)

Solve the following equation :

$x$ + 5 = 10

Answer

⇒ $x$ + 5 = 10

Transposing 5 to R.H.S.,

⇒ $x$ = 10 − 5

⇒ $x$ = 5

Hence, $\bm{x}$ = 5.

Solve the following equation :

2 + $y$ = 7

Answer

⇒ 2 + $y$ = 7

Transposing 2 to R.H.S.,

⇒ $y$ = 7 − 2

⇒ $y$ = 5

Hence, $\bm{y}$ = 5.

Solve the following equation :

$a$ − 2 = 6

Answer

⇒ $a$ − 2 = 6

Transposing −2 to R.H.S.,

⇒ $a$ = 6 + 2

⇒ $a$ = 8

Hence, $\bm{a}$ = 8.

Solve the following equation :

$x$ − 5 = 8

Answer

⇒ $x$ − 5 = 8

Transposing −5 to R.H.S.,

⇒ $x$ = 8 + 5

⇒ $x$ = 13

Hence, $\bm{x}$ = 13.

Solve the following equation :

5 − $d$ = 12

Answer

⇒ 5 − $d$ = 12

Transposing 5 to R.H.S.,

⇒ −$d$ = 12 − 5

⇒ −$d$ = 7

Multiplying both sides by −1,

⇒ (−$d$) × (−1) = 7 × (−1)

⇒ $d$ = −7

Hence, $\bm{d}$ = −7.

Solve the following equation :

$3p$ = 12

Answer

⇒ $3p$ = 12

Dividing both sides by 3,

⇒ $\dfrac{3p}{3} = \dfrac{12}{3}$

⇒ $p$ = 4

Hence, $\bm{p}$ = 4.

Solve the following equation :

14 = $7m$

Answer

⇒ 14 = $7m$

Dividing both sides by 7,

⇒ $\dfrac{14}{7} = \dfrac{7m}{7}$

⇒ 2 = $m$

Hence, $\bm{m}$ = 2.

Solve the following equation :

$2x$ = 0

Answer

⇒ $2x$ = 0

Dividing both sides by 2,

⇒ $\dfrac{2x}{2} = \dfrac{0}{2}$

⇒ $x$ = 0

Hence, $\bm{x}$ = 0.

Solve the following equation :

$\dfrac{x}{9} = 2$

Answer

⇒ $\dfrac{x}{9} = 2$

Multiplying both sides by 9,

⇒ $\dfrac{x}{9} \times 9$ = 2 × 9

⇒ $x$ = 18

Hence, $\bm{x}$ = 18.

Solve the following equation :

$\dfrac{y}{-12} = -4$

Answer

⇒ $\dfrac{y}{-12} = -4$

Multiplying both sides by −12,

⇒ $\dfrac{y}{-12} \times (-12)$ = (−4) × (−12)

⇒ $y$ = 48

Hence, $\bm{y}$ = 48.

Solve the following equation :

$8x$ − 2 = 38

Answer

⇒ $8x$ − 2 = 38

Transposing −2 to R.H.S.,

⇒ $8x$ = 38 + 2

⇒ $8x$ = 40

Dividing both sides by 8,

⇒ $\dfrac{8x}{8} = \dfrac{40}{8}$

⇒ $x$ = 5

Hence, $\bm{x}$ = 5.

Solve the following equation :

$2x$ + 5 = 5

Answer

⇒ $2x$ + 5 = 5

Transposing 5 to R.H.S.,

⇒ $2x$ = 5 − 5

⇒ $2x$ = 0

Dividing both sides by 2,

⇒ $\dfrac{2x}{2} = \dfrac{0}{2}$

⇒ $x$ = 0

Hence, $\bm{x}$ = 0.

Solve the following equation :

$5x$ − 1 = 74

Answer

⇒ $5x$ − 1 = 74

Transposing −1 to R.H.S.,

⇒ $5x$ = 74 + 1

⇒ $5x$ = 75

Dividing both sides by 5,

⇒ $\dfrac{5x}{5} = \dfrac{75}{5}$

⇒ $x$ = 15

Hence, $\bm{x}$ = 15.

Solve the following equation :

14 = 27 − $x$

Answer

⇒ 14 = 27 − $x$

Transposing −$x$ to L.H.S. and 14 to R.H.S.,

⇒ $x$ = 27 − 14

⇒ $x$ = 13

Hence, $\bm{x}$ = 13.

Solve the following equation :

10 + $6a$ = 40

Answer

⇒ 10 + $6a$ = 40

Transposing 10 to R.H.S.,

⇒ $6a$ = 40 − 10

⇒ $6a$ = 30

Dividing both sides by 6,

⇒ $\dfrac{6a}{6} = \dfrac{30}{6}$

⇒ $a$ = 5

Hence, $\bm{a}$ = 5.

Solve the following equation :

$c - \dfrac{1}{2} = \dfrac{1}{3}$

Answer

⇒ $c - \dfrac{1}{2} = \dfrac{1}{3}$

Transposing $-\dfrac{1}{2}$ to R.H.S.,

⇒ $c = \dfrac{1}{3} + \dfrac{1}{2}$

⇒ $c = \dfrac{2 + 3}{6}$

⇒ $c = \dfrac{5}{6}$

⇒ $c$ = $\dfrac{5}{6}$

Hence, $\bm{c}$ = $\dfrac{5}{6}$.

Solve the following equation :

$\dfrac{a}{15} - 2 = 0$

Answer

⇒ $\dfrac{a}{15} - 2 = 0$

Transposing −2 to R.H.S.,

⇒ $\dfrac{a}{15} = 2$

Multiplying both sides by 15,

⇒ $\dfrac{a}{15} \times 15$ = 2 × 15

⇒ $a$ = 30

Hence, $\bm{a}$ = 30.

Solve the following equation :

12 = $c$ − 2

Answer

⇒ 12 = $c$ − 2

Transposing −2 to L.H.S.,

⇒ 12 + 2 = $c$

⇒ 14 = $c$

Hence, $\bm{c}$ = 14.

Solve the following equation :

4 = $x$ − 2.5

Answer

⇒ 4 = $x$ − 2.5

Transposing −2.5 to L.H.S.,

⇒ 4 + 2.5 = $x$

⇒ 6.5 = $x$

Hence, $\bm{x}$ = 6.5.

Solve the following equation :

$y + 5 = 8\dfrac{1}{4}$

Answer

⇒ $y + 5 = 8\dfrac{1}{4}$

⇒ $y + 5 = \dfrac{33}{4}$

Transposing 5 to R.H.S.,

⇒ $y = \dfrac{33}{4} - 5$

⇒ $y = \dfrac{33 - 20}{4}$

⇒ $y = \dfrac{13}{4} = 3\dfrac{1}{4}$

Hence, $\bm{y}$ = $3\dfrac{1}{4}$.

Solve the following equation :

$x + \dfrac{1}{4} = -\dfrac{3}{8}$

Answer

⇒ $x + \dfrac{1}{4} = -\dfrac{3}{8}$

Transposing $\dfrac{1}{4}$ to R.H.S.,

⇒ $x = -\dfrac{3}{8} - \dfrac{1}{4}$

⇒ $x = \dfrac{-3 - 2}{8}$

⇒ $x = -\dfrac{5}{8}$

Hence, $\bm{x}$ = $-\dfrac{5}{8}$.

Solve the following equation :

$p$ + 0.02 = 0.08

Answer

⇒ $p$ + 0.02 = 0.08

Transposing 0.02 to R.H.S.,

⇒ $p$ = 0.08 − 0.02

⇒ $p$ = 0.06

Hence, $\bm{p}$ = 0.06.

Solve the following equation :

$p - 12 = 2\dfrac{2}{3}$

Answer

⇒ $p - 12 = 2\dfrac{2}{3}$

⇒ $p - 12 = \dfrac{8}{3}$

Transposing −12 to R.H.S.,

⇒ $p = \dfrac{8}{3} + 12$

⇒ $p = \dfrac{8 + 36}{3}$

⇒ $p = \dfrac{44}{3} = 14\dfrac{2}{3}$

Hence, $\bm{p}$ = $14\dfrac{2}{3}$.

Solve the following equation :

−$3x$ = 15

Answer

⇒ −$3x$ = 15

Dividing both sides by −3,

⇒ $\dfrac{-3x}{-3} = \dfrac{15}{-3}$

⇒ $x$ = −5

Hence, $\bm{x}$ = −5.

Solve the following equation :

$1.3b$ = 39

Answer

⇒ $1.3b$ = 39

Dividing both sides by 1.3,

⇒ $b = \dfrac{39}{1.3} = \dfrac{390}{13}$

⇒ $b$ = 30

Hence, $\bm{b}$ = 30.

Solve the following equation :

$\dfrac{5}{8}n = 20$

Answer

⇒ $\dfrac{5}{8}n = 20$

Multiplying both sides by $\dfrac{8}{5}$,

⇒ $\dfrac{5}{8}n \times \dfrac{8}{5} = 20 \times \dfrac{8}{5}$

⇒ $n$ = 4 × 8 = 32

Hence, $\bm{n}$ = 32.

Solve the following equation :

$\dfrac{3}{16}m = 21$

Answer

⇒ $\dfrac{3}{16}m = 21$

Multiplying both sides by $\dfrac{16}{3}$,

⇒ $\dfrac{3}{16}m \times \dfrac{16}{3} = 21 \times \dfrac{16}{3}$

⇒ $m$ = 7 × 16 = 112

Hence, $\bm{m}$ = 112.

Solve the following equation :

$2a$ − 3 = 5

Answer

⇒ $2a$ − 3 = 5

Transposing −3 to R.H.S.,

⇒ $2a$ = 5 + 3

⇒ $2a$ = 8

Dividing both sides by 2,

⇒ $\dfrac{2a}{2} = \dfrac{8}{2}$

⇒ $a$ = 4

Hence, $\bm{a}$ = 4.

Solve the following equation :

$3p$ − 1 = 8

Answer

⇒ $3p$ − 1 = 8

Transposing −1 to R.H.S.,

⇒ $3p$ = 8 + 1

⇒ $3p$ = 9

Dividing both sides by 3,

⇒ $\dfrac{3p}{3} = \dfrac{9}{3}$

⇒ $p$ = 3

Hence, $\bm{p}$ = 3.

Solve the following equation :

$9y$ − 7 = 20

Answer

⇒ $9y$ − 7 = 20

Transposing −7 to R.H.S.,

⇒ $9y$ = 20 + 7

⇒ $9y$ = 27

Dividing both sides by 9,

⇒ $\dfrac{9y}{9} = \dfrac{27}{9}$

⇒ $y$ = 3

Hence, $\bm{y}$ = 3.

Solve the following equation :

$2b$ − 14 = 8

Answer

⇒ $2b$ − 14 = 8

Transposing −14 to R.H.S.,

⇒ $2b$ = 8 + 14

⇒ $2b$ = 22

Dividing both sides by 2,

⇒ $\dfrac{2b}{2} = \dfrac{22}{2}$

⇒ $b$ = 11

Hence, $\bm{b}$ = 11.

Solve the following equation :

$\dfrac{7}{10}x + 6 = 41$

Answer

⇒ $\dfrac{7}{10}x + 6 = 41$

Transposing 6 to R.H.S.,

⇒ $\dfrac{7}{10}x = 41 - 6$

⇒ $\dfrac{7}{10}x = 35$

Multiplying both sides by $\dfrac{10}{7}$,

⇒ $\dfrac{7}{10}x \times \dfrac{10}{7} = 35 \times \dfrac{10}{7}$

⇒ $x$ = 5 × 10 = 50

Hence, $\bm{x}$ = 50.

Solve the following equation :

$\dfrac{5}{12}m - 12 = 48$

Answer

⇒ $\dfrac{5}{12}m - 12 = 48$

Transposing −12 to R.H.S.,

⇒ $\dfrac{5}{12}m = 48 + 12$

⇒ $\dfrac{5}{12}m = 60$

Multiplying both sides by $\dfrac{12}{5}$,

⇒ $\dfrac{5}{12}m \times \dfrac{12}{5} = 60 \times \dfrac{12}{5}$

⇒ $m$ = 12 × 12 = 144

Hence, $\bm{m}$ = 144.