Simple Linear Equations — Exercise 14(B)

Solve :

$8y - 4y$ = 20

Answer

Solving,

$\Rightarrow 8y - 4y = 20 \\[1em] \Rightarrow 4y = 20 \\[1em] \Rightarrow y = \dfrac{20}{4} \\[1em] \Rightarrow y = 5.$

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

Solve :

$9b - 4b + 3b$ = 16

Answer

Solving,

$\Rightarrow 9b - 4b + 3b = 16 \\[1em] \Rightarrow (9 - 4 + 3)b = 16 \\[1em] \Rightarrow 8b = 16 \\[1em] \Rightarrow b = \dfrac{16}{8} \\[1em] \Rightarrow b = 2.$

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

Solve :

$5y + 8 = 8y - 18$

Answer

Solving,

$\Rightarrow 5y + 8 = 8y - 18 \\[1em] \Rightarrow 5y - 8y = -18 - 8 \\[1em] \Rightarrow -3y = -26 \\[1em] \Rightarrow y = \dfrac{-26}{-3} \\[1em] \Rightarrow y = \dfrac{26}{3} \\[1em] \Rightarrow y = 8\dfrac{2}{3}.$

Hence, $\bm{y}$ = $8\dfrac{2}{3}$.

Solve :

$6 = 7 + 2p - 5$

Answer

Solving,

$\Rightarrow 6 = 7 + 2p - 5 \\[1em] \Rightarrow 6 = 2 + 2p \\[1em] \Rightarrow 6 - 2 = 2p \\[1em] \Rightarrow 4 = 2p \\[1em] \Rightarrow \dfrac{4}{2} = \dfrac{2p}{2} \\[1em] \Rightarrow p = 2.$

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

Solve :

$8 - 7x = 13x + 8$

Answer

Solving,

$\Rightarrow 8 - 7x = 13x + 8 \\[1em] \Rightarrow -7x - 13x = 8 - 8 \\[1em] \Rightarrow -20x = 0 \\[1em] \Rightarrow x = 0.$

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

Solve :

$4x - 5x + 2x = 28 + 3x$

Answer

Solving,

$\Rightarrow 4x - 5x + 2x = 28 + 3x \\[1em] \Rightarrow (4 - 5 + 2)x = 28 + 3x \\[1em] \Rightarrow x = 28 + 3x \\[1em] \Rightarrow x - 3x = 28 \\[1em] \Rightarrow -2x = 28 \\[1em] \Rightarrow x = \dfrac{28}{-2} \\[1em] \Rightarrow x = -14.$

Hence, $\bm{x}$ = −14.

Solve :

$9 + m = 6m + 8 - m$

Answer

Solving,

$\Rightarrow 9 + m = 6m + 8 - m \\[1em] \Rightarrow 9 + m = 5m + 8 \\[1em] \Rightarrow m - 5m = 8 - 9 \\[1em] \Rightarrow -4m = -1 \\[1em] \Rightarrow m = \dfrac{-1}{-4} \\[1em] \Rightarrow m = \dfrac{1}{4}.$

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

Solve :

24 = $y + 2y + 3 + 4y$

Answer

Solving,

$\Rightarrow 24 = y + 2y + 3 + 4y \\[1em] \Rightarrow 24 = 7y + 3 \\[1em] \Rightarrow 24 - 3 = 7y \\[1em] \Rightarrow 21 = 7y \\[1em] \Rightarrow \dfrac{21}{7} = \dfrac{7y}{7} \\[1em] \Rightarrow y = 3.$

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

Solve :

$19x + 13 - 12x + 3$ = 23

Answer

Solving,

$\Rightarrow 19x + 13 - 12x + 3 = 23 \\[1em] \Rightarrow (19 - 12)x + (13 + 3) = 23 \\[1em] \Rightarrow 7x + 16 = 23 \\[1em] \Rightarrow 7x = 23 - 16 \\[1em] \Rightarrow 7x = 7 \\[1em] \Rightarrow x = \dfrac{7}{7} \\[1em] \Rightarrow x = 1.$

Hence, $\bm{x}$ = 1.

Solve :

$6b + 40 = -100 - b$

Answer

Solving,

$\Rightarrow 6b + 40 = -100 - b \\[1em] \Rightarrow 6b + b = -100 - 40 \\[1em] \Rightarrow 7b = -140 \\[1em] \Rightarrow b = \dfrac{-140}{7} \\[1em] \Rightarrow b = -20.$

Hence, $\bm{b}$ = −20.

Solve :

$6 - 5m - 1 + 3m$ = 0

Answer

Solving,

$\Rightarrow 6 - 5m - 1 + 3m = 0 \\[1em] \Rightarrow (6 - 1) + (-5 + 3)m = 0 \\[1em] \Rightarrow 5 - 2m = 0 \\[1em] \Rightarrow -2m = -5 \\[1em] \Rightarrow m = \dfrac{-5}{-2} \\[1em] \Rightarrow m = \dfrac{5}{2} \\[1em] \Rightarrow m = 2\dfrac{1}{2}.$

Hence, $\bm{m}$ = $2\dfrac{1}{2}$.

Solve :

$0·4x - 1·2 = 0·3x + 0·6$

Answer

Solving,

$\Rightarrow 0.4x - 1.2 = 0.3x + 0.6 \\[1em] \Rightarrow 0.4x - 0.3x = 0.6 + 1.2 \\[1em] \Rightarrow 0.1x = 1.8 \\[1em] \Rightarrow x = \dfrac{1.8}{0.1} \\[1em] \Rightarrow x = \dfrac{18}{1} \\[1em] \Rightarrow x = 18.$

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

Solve :

$6(x + 4)$ = 36

Answer

Solving,

$\Rightarrow 6(x + 4) = 36 \\[1em] \Rightarrow (x + 4) = \dfrac{36}{6} \\[1em] \Rightarrow x + 4 = 6 \\[1em] \Rightarrow x = 6 - 4 \\[1em] \Rightarrow x = 2.$

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

Solve :

$9(a + 5) + 2$ = 11

Answer

Solving,

$\Rightarrow 9(a + 5) + 2 = 11 \\[1em] \Rightarrow 9(a + 5) = 11 - 2 \\[1em] \Rightarrow 9(a + 5) = 9 \\[1em] \Rightarrow (a + 5) = \dfrac{9}{9} \\[1em] \Rightarrow a + 5 = 1 \\[1em] \Rightarrow a = 1 - 5 \\[1em] \Rightarrow a = -4.$

Hence, $\bm{a}$ = −4.

Solve :

$4(x - 2)$ = 12

Answer

Solving,

$\Rightarrow 4(x - 2) = 12 \\[1em] \Rightarrow (x - 2) = \dfrac{12}{4} \\[1em] \Rightarrow x - 2 = 3 \\[1em] \Rightarrow x = 3 + 2 \\[1em] \Rightarrow x = 5.$

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

Solve :

$-3(a - 6)$ = 24

Answer

Solving,

$\Rightarrow -3(a - 6) = 24 \\[1em] \Rightarrow (a - 6) = \dfrac{24}{-3} \\[1em] \Rightarrow a - 6 = -8 \\[1em] \Rightarrow a = -8 + 6 \\[1em] \Rightarrow a = -2.$

Hence, $\bm{a}$ = −2.

Solve :

$7(x - 2) = 2(2x - 4)$

Answer

Solving,

$\Rightarrow 7(x - 2) = 2(2x - 4) \\[1em] \Rightarrow 7x - 14 = 4x - 8 \\[1em] \Rightarrow 7x - 4x = -8 + 14 \\[1em] \Rightarrow 3x = 6 \\[1em] \Rightarrow x = \dfrac{6}{3} \\[1em] \Rightarrow x = 2.$

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

Solve :

$(x - 4) (2x + 3) = 2x^{2}$

Answer

Solving,

$\Rightarrow (x - 4)(2x + 3) = 2x^{2} \\[1em] \Rightarrow 2x^{2} + 3x - 8x - 12 = 2x^{2} \\[1em] \Rightarrow 2x^{2} - 5x - 12 = 2x^{2} \\[1em] \Rightarrow -5x - 12 = 2x^{2} - 2x^{2} \\[1em] \Rightarrow -5x - 12 = 0 \\[1em] \Rightarrow -5x = 12 \\[1em] \Rightarrow x = \dfrac{12}{-5} \\[1em] \Rightarrow x = -\dfrac{12}{5} \\[1em] \Rightarrow x = -2\dfrac{2}{5}.$

Hence, $\bm{x}$ = $-2\dfrac{2}{5}$.

Solve :

$21 - 3(b - 7) = b + 20$

Answer

Solving,

$\Rightarrow 21 - 3(b - 7) = b + 20 \\[1em] \Rightarrow 21 - 3b + 21 = b + 20 \\[1em] \Rightarrow 42 - 3b = b + 20 \\[1em] \Rightarrow -3b - b = 20 - 42 \\[1em] \Rightarrow -4b = -22 \\[1em] \Rightarrow b = \dfrac{-22}{-4} \\[1em] \Rightarrow b = \dfrac{11}{2} \\[1em] \Rightarrow b = 5\dfrac{1}{2}.$

Hence, $\bm{b}$ = $5\dfrac{1}{2}$.

Solve :

$x(x + 5) = x^{2} + x + 32$

Answer

Solving,

$\Rightarrow x(x + 5) = x^{2} + x + 32 \\[1em] \Rightarrow x^{2} + 5x = x^{2} + x + 32 \\[1em] \Rightarrow x^{2} - x^{2} + 5x - x = 32 \\[1em] \Rightarrow 4x = 32 \\[1em] \Rightarrow x = \dfrac{32}{4} \\[1em] \Rightarrow x = 8.$

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