Simple Equations — Exercise 13(A)

Solve:

$x - 4 = 8$

Answer

Solving,

$\Rightarrow x - 4 = 8 \\[1em] \text{ [Adding 4 on each side] } \\[1em] \Rightarrow x - 4 + 4 = 8 + 4 \\[1em] \Rightarrow x + 0 = 12 \\[1em] \Rightarrow x = 12$

Hence, $\bm{x = 12}$.

Solve:

$x + 7 = 2$

Answer

Solving,

$\Rightarrow x + 7 = 2 \\[1em] \text{ [Subtracting 7 from each side] } \\[1em] \Rightarrow x + 7 - 7 = 2 - 7 \\[1em] \Rightarrow x + 0 = -5 \\[1em] \Rightarrow x = -5$

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

Solve:

$x - 6 = -3$

Answer

Solving,

$\Rightarrow x - 6 = -3 \\[1em] \text{ [Adding 6 on each side] } \\[1em] \Rightarrow x - 6 + 6 = -3 + 6 \\[1em] \Rightarrow x + 0 = 3 \\[1em] \Rightarrow x = 3$

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

Solve:

$y + 2 = -6$

Answer

Solving,

$\Rightarrow y + 2 = -6 \\[1em] \text{ [Subtracting 2 from each side] } \\[1em] \Rightarrow y + 2 - 2 = -6 - 2 \\[1em] \Rightarrow y + 0 = -8 \\[1em] \Rightarrow y = -8$

Hence, $\bm{y = -8}$.

Solve:

$x + 3 = -1$

Answer

Solving,

$\Rightarrow x + 3 = -1 \\[1em] \text{ [Subtracting 3 from each side] } \\[1em] \Rightarrow x + 3 - 3 = -1 - 3 \\[1em] \Rightarrow x + 0 = -4 \\[1em] \Rightarrow x = -4$

Hence, $\bm{x = -4}$.

Solve:

$z - 5 = -8$

Answer

Solving,

$\Rightarrow z - 5 = -8 \\[1em] \text{ [Adding 5 on each side] } \\[1em] \Rightarrow z - 5 + 5 = -8 + 5 \\[1em] \Rightarrow z + 0 = -3 \\[1em] \Rightarrow z = -3$

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

Solve:

$\dfrac{x}{3} = 6$

Answer

Solving,

$\Rightarrow \dfrac{x}{3} = 6 \\[1em] \text{ [Multiplying each side by 3] } \\[1em] \Rightarrow \dfrac{x}{3} \times 3 = 6 \times 3 \\[1em] \Rightarrow x = 18$

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

Solve:

$\dfrac{y}{2} = -4$

Answer

Solving,

$\Rightarrow \dfrac{y}{2} = -4 \\[1em] \text{ [Multiplying each side by 2] } \\[1em] \Rightarrow \dfrac{y}{2} \times 2 = -4 \times 2 \\[1em] \Rightarrow y = -8$

Hence, $\bm{y = -8}$.

Solve:

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

Answer

Solving,

$\Rightarrow \dfrac{2x}{4} = 3 \\[1em] \Rightarrow \dfrac{x}{2} = 3 \\[1em] \text{ [Multiplying each side by 2] } \\[1em] \Rightarrow \dfrac{x}{2} \times 2 = 3 \times 2 \\[1em] \Rightarrow x = 6$

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

Solve:

$2x = 10$

Answer

Solving,

$\Rightarrow 2x = 10 \\[1em] \text{ [Dividing each side by 2] } \\[1em] \Rightarrow \dfrac{2x}{2} = \dfrac{10}{2} \\[1em] \Rightarrow x = 5$

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

Solve:

$3y = -12$

Answer

Solving,

$\Rightarrow 3y = -12 \\[1em] \text{ [Dividing each side by 3] } \\[1em] \Rightarrow \dfrac{3y}{3} = \dfrac{-12}{3} \\[1em] \Rightarrow y = -4$

Hence, $\bm{y = -4}$.

Solve:

$2x - 3 = 7$

Answer

Solving,

$\Rightarrow 2x - 3 = 7 \\[1em] \text{ [Adding 3 on each side] } \\[1em] \Rightarrow 2x - 3 + 3 = 7 + 3 \\[1em] \Rightarrow 2x = 10 \\[1em] \text{ [Dividing each side by 2] } \\[1em] \Rightarrow \dfrac{2x}{2} = \dfrac{10}{2} \\[1em] \Rightarrow x = 5$

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

Solve:

$3x - 5 = 4$

Answer

Solving,

$\Rightarrow 3x - 5 = 4 \\[1em] \text{ [Adding 5 on each side] } \\[1em] \Rightarrow 3x - 5 + 5 = 4 + 5 \\[1em] \Rightarrow 3x = 9 \\[1em] \text{ [Dividing each side by 3] } \\[1em] \Rightarrow \dfrac{3x}{3} = \dfrac{9}{3} \\[1em] \Rightarrow x = 3$

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

Solve:

$4x - 1 = 7$

Answer

Solving,

$\Rightarrow 4x - 1 = 7 \\[1em] \text{ [Adding 1 on each side] } \\[1em] \Rightarrow 4x - 1 + 1 = 7 + 1 \\[1em] \Rightarrow 4x = 8 \\[1em] \text{ [Dividing each side by 4] } \\[1em] \Rightarrow \dfrac{4x}{4} = \dfrac{8}{4} \\[1em] \Rightarrow x = 2$

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

Solve:

$5z - 3 = 2$

Answer

Solving,

$\Rightarrow 5z - 3 = 2 \\[1em] \text{ [Adding 3 on each side] } \\[1em] \Rightarrow 5z - 3 + 3 = 2 + 3 \\[1em] \Rightarrow 5z = 5 \\[1em] \text{ [Dividing each side by 5] } \\[1em] \Rightarrow \dfrac{5z}{5} = \dfrac{5}{5} \\[1em] \Rightarrow z = 1$

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

Solve:

$2x - 3 = -5$

Answer

Solving,

$\Rightarrow 2x - 3 = -5 \\[1em] \text{ [Adding 3 on each side] } \\[1em] \Rightarrow 2x - 3 + 3 = -5 + 3 \\[1em] \Rightarrow 2x = -2 \\[1em] \text{ [Dividing each side by 2] } \\[1em] \Rightarrow \dfrac{2x}{2} = \dfrac{-2}{2} \\[1em] \Rightarrow x = -1$

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

Solve:

$4y + 5 = -3$

Answer

Solving,

$\Rightarrow 4y + 5 = -3 \\[1em] \text{ [Subtracting 5 from each side] } \\[1em] \Rightarrow 4y + 5 - 5 = -3 - 5 \\[1em] \Rightarrow 4y = -8 \\[1em] \text{ [Dividing each side by 4] } \\[1em] \Rightarrow \dfrac{4y}{4} = \dfrac{-8}{4} \\[1em] \Rightarrow y = -2$

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

Solve:

$6z - 8 = 1$

Answer

Solving,

$\Rightarrow 6z - 8 = 1 \\[1em] \text{ [Adding 8 on each side] } \\[1em] \Rightarrow 6z - 8 + 8 = 1 + 8 \\[1em] \Rightarrow 6z = 9 \\[1em] \text{ [Dividing each side by 6] } \\[1em] \Rightarrow \dfrac{6z}{6} = \dfrac{9}{6} \\[1em] \Rightarrow z = \dfrac{3}{2}$

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