Simple Equations — Exercise 13(B)

Solve:

$5x + 4 = 19$

Answer

Solving,

$\Rightarrow 5x + 4 = 19 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 5x = 19 - 4 \\[1em] \Rightarrow 5x = 15 \\[1em] \text{ [Dividing each side by 5] } \\[1em] \Rightarrow x = \dfrac{15}{5} \\[1em] \Rightarrow x = 3.$

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

Solve:

$3x - 8 = 10$

Answer

Solving,

$\Rightarrow 3x - 8 = 10 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 3x = 10 + 8 \\[1em] \Rightarrow 3x = 18 \\[1em] \text{ [Dividing each side by 3] } \\[1em] \Rightarrow x = \dfrac{18}{3} \\[1em] \Rightarrow x = 6.$

Hence, $\bm{x = 6}$.

Solve:

$5 - 2y = 9$

Answer

Solving,

$\Rightarrow 5 - 2y = 9 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow -2y = 9 - 5 \\[1em] \Rightarrow -2y = 4 \\[1em] \text{ [Dividing each side by −2] } \\[1em] \Rightarrow y = \dfrac{4}{-2} \\[1em] \Rightarrow y = -2.$

Hence, $\bm{y = -2}$.

Solve:

$-6 + 3x = -5$

Answer

Solving,

$\Rightarrow -6 + 3x = -5 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 3x = -5 + 6 \\[1em] \Rightarrow 3x = 1 \\[1em] \text{ [Dividing each side by 3] } \\[1em] \Rightarrow x = \dfrac{1}{3}.$

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

Solve:

$2x + 12 = 3 - x$

Answer

Solving,

$\Rightarrow 2x + 12 = 3 - x \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 2x + x = 3 - 12 \\[1em] \Rightarrow 3x = -9 \\[1em] \text{ [Dividing each side by 3] } \\[1em] \Rightarrow x = \dfrac{-9}{3} \\[1em] \Rightarrow x = -3.$

Hence, $\bm{x = -3}$.

Solve:

$2 - 5y = 2y - 5$

Answer

Solving,

$\Rightarrow 2 - 5y = 2y - 5 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow -5y - 2y = -5 - 2 \\[1em] \Rightarrow -7y = -7 \\[1em] \text{ [Dividing each side by −7] } \\[1em] \Rightarrow y = \dfrac{-7}{-7} \\[1em] \Rightarrow y = 1.$

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

Solve:

$\dfrac{x}{5} + 5 = 2$

Answer

Solving,

$\Rightarrow \dfrac{x}{5} + 5 = 2 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow \dfrac{x}{5} = 2 - 5 \\[1em] \Rightarrow \dfrac{x}{5} = -3 \\[1em] \text{ [Multiplying each side by 5] } \\[1em] \Rightarrow x = -3 \times 5 \\[1em] \Rightarrow x = -15.$

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

Solve:

$\dfrac{4x}{3} + 3 = x - 2$

Answer

Solving,

$\Rightarrow \dfrac{4x}{3} + 3 = x - 2 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow \dfrac{4x}{3} - x = -2 - 3 \\[1em] \text{ [Taking L.C.M.] } \\[1em] \Rightarrow \dfrac{4x - 3x}{3} = -5 \\[1em] \Rightarrow \dfrac{x}{3} = -5 \\[1em] \text{ [Multiplying each side by 3] } \\[1em] \Rightarrow x = -5 \times 3 \\[1em] \Rightarrow x = -15.$

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

Solve:

$\dfrac{3x + 2}{5} = 4$

Answer

Solving,

$\Rightarrow \dfrac{3x + 2}{5} = 4 \\[1em] \text{ [Multiplying each side by 5] } \\[1em] \Rightarrow 3x + 2 = 4 \times 5 \\[1em] \Rightarrow 3x + 2 = 20 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 3x = 20 - 2 \\[1em] \Rightarrow 3x = 18 \\[1em] \text{ [Dividing each side by 3] } \\[1em] \Rightarrow x = \dfrac{18}{3} \\[1em] \Rightarrow x = 6.$

Hence, $\bm{x = 6}$.

Solve:

$\dfrac{x}{2} - 6 = \dfrac{x}{3} - 5$

Answer

Solving,

$\Rightarrow \dfrac{x}{2} - 6 = \dfrac{x}{3} - 5 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow \dfrac{x}{2} - \dfrac{x}{3} = -5 + 6 \\[1em] \text{ [Taking L.C.M.] } \\[1em] \Rightarrow \dfrac{3x - 2x}{6} = 1 \\[1em] \Rightarrow \dfrac{x}{6} = 1 \\[1em] \text{ [Multiplying each side by 6] } \\[1em] \Rightarrow x = 6.$

Hence, $\bm{x = 6}$.

Solve:

$\dfrac{2y}{3} - 8 = 2 - y$

Answer

Solving,

$\Rightarrow \dfrac{2y}{3} - 8 = 2 - y \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow \dfrac{2y}{3} + y = 2 + 8 \\[1em] \text{ [Taking L.C.M.] } \\[1em] \Rightarrow \dfrac{2y + 3y}{3} = 10 \\[1em] \Rightarrow \dfrac{5y}{3} = 10 \\[1em] \text{ [Multiplying each side by 3] } \\[1em] \Rightarrow 5y = 30 \\[1em] \text{ [Dividing each side by 5] } \\[1em] \Rightarrow y = \dfrac{30}{5} \\[1em] \Rightarrow y = 6.$

Hence, $\bm{y = 6}$.

Solve:

$\dfrac{x}{2} + 2 = 5 - x$

Answer

Solving,

$\Rightarrow \dfrac{x}{2} + 2 = 5 - x \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow \dfrac{x}{2} + x = 5 - 2 \\[1em] \text{ [Taking L.C.M.] } \\[1em] \Rightarrow \dfrac{x + 2x}{2} = 3 \\[1em] \Rightarrow \dfrac{3x}{2} = 3 \\[1em] \text{ [Multiplying each side by 2] } \\[1em] \Rightarrow 3x = 6 \\[1em] \text{ [Dividing each side by 3] } \\[1em] \Rightarrow x = \dfrac{6}{3} \\[1em] \Rightarrow x = 2.$

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

Solve:

$6(2x - 1) - 5(x - 3) = 2(x + 2)$

Answer

Solving,

$\Rightarrow 6(2x - 1) - 5(x - 3) = 2(x + 2) \\[1em] \text{ [Removing brackets] } \\[1em] \Rightarrow 12x - 6 - 5x + 15 = 2x + 4 \\[1em] \Rightarrow 7x + 9 = 2x + 4 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 7x - 2x = 4 - 9 \\[1em] \Rightarrow 5x = -5 \\[1em] \text{ [Dividing each side by 5] } \\[1em] \Rightarrow x = \dfrac{-5}{5} \\[1em] \Rightarrow x = -1.$

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

Solve:

$7(3x - 1) - 6(2x + 3) = 8(x - 2) + 1$

Answer

Solving,

$\Rightarrow 7(3x - 1) - 6(2x + 3) = 8(x - 2) + 1 \\[1em] \text{ [Removing brackets] } \\[1em] \Rightarrow 21x - 7 - 12x - 18 = 8x - 16 + 1 \\[1em] \Rightarrow 9x - 25 = 8x - 15 \\[1em] \text{ [By transposition] } \\[1em] \Rightarrow 9x - 8x = -15 + 25 \\[1em] \Rightarrow x = 10.$

Hence, $\bm{x = 10}$.