Framing Algebraic Expressions — Exercise 13(D)

Solve :

$2x + 5 = 17$

Answer

Solving,

$\Rightarrow 2x + 5 = 17 \\[1em] \Rightarrow 2x = 17 - 5 \\[1em] \Rightarrow 2x = 12 \\[1em] \Rightarrow x = \dfrac{12}{2} \\[1em] \Rightarrow x = 6.$

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

Solve :

$3y - 2 = 1$

Answer

Solving,

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

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

Solve :

$5p + 4 = 29$

Answer

Solving,

$\Rightarrow 5p + 4 = 29 \\[1em] \Rightarrow 5p = 29 - 4 \\[1em] \Rightarrow 5p = 25 \\[1em] \Rightarrow p = \dfrac{25}{5} \\[1em] \Rightarrow p = 5.$

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

Solve :

$4a - 3 = -27$

Answer

Solving,

$\Rightarrow 4a - 3 = -27 \\[1em] \Rightarrow 4a = -27 + 3 \\[1em] \Rightarrow 4a = -24 \\[1em] \Rightarrow a = \dfrac{-24}{4} \\[1em] \Rightarrow a = -6.$

Hence, $\bm{a} = -6$.

Solve :

$2z + 3 = -19$

Answer

Solving,

$\Rightarrow 2z + 3 = -19 \\[1em] \Rightarrow 2z = -19 - 3 \\[1em] \Rightarrow 2z = -22 \\[1em] \Rightarrow z = \dfrac{-22}{2} \\[1em] \Rightarrow z = -11.$

Hence, $\bm{z} = -11$.

Solve :

$7m - 1 = 20$

Answer

Solving,

$\Rightarrow 7m - 1 = 20 \\[1em] \Rightarrow 7m = 20 + 1 \\[1em] \Rightarrow 7m = 21 \\[1em] \Rightarrow m = \dfrac{21}{7} \\[1em] \Rightarrow m = 3.$

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

Solve :

$2.4x - 3 = 4.2$

Answer

Solving,

$\Rightarrow 2.4x - 3 = 4.2 \\[1em] \Rightarrow 2.4x = 4.2 + 3 \\[1em] \Rightarrow 2.4x = 7.2 \\[1em] \Rightarrow x = \dfrac{7.2}{2.4} \\[1em] \Rightarrow x = 3.$

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

Solve :

$4m + 9.4 = 5$

Answer

Solving,

$\Rightarrow 4m + 9.4 = 5 \\[1em] \Rightarrow 4m = 5 - 9.4 \\[1em] \Rightarrow 4m = -4.4 \\[1em] \Rightarrow m = \dfrac{-4.4}{4} \\[1em] \Rightarrow m = -1.1.$

Hence, $\bm{m} = -1.1$.

Solve :

$6y + 4 = -4.4$

Answer

Solving,

$\Rightarrow 6y + 4 = -4.4 \\[1em] \Rightarrow 6y = -4.4 - 4 \\[1em] \Rightarrow 6y = -8.4 \\[1em] \Rightarrow y = \dfrac{-8.4}{6} \\[1em] \Rightarrow y = -1.4.$

Hence, $\bm{y} = -1.4$.

Solve :

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

Answer

Solving,

$\Rightarrow \dfrac{x}{3} - 5 = 2 \\[1em] \Rightarrow \dfrac{x}{3} = 2 + 5 \\[1em] \Rightarrow \dfrac{x}{3} = 7 \\[1em] \Rightarrow x = 7 \times 3 \\[1em] \Rightarrow x = 21.$

Hence, $\bm{x} = 21$.

Solve :

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

Answer

Solving,

$\Rightarrow \dfrac{y}{2} - 3 = 8 \\[1em] \Rightarrow \dfrac{y}{2} = 8 + 3 \\[1em] \Rightarrow \dfrac{y}{2} = 11 \\[1em] \Rightarrow y = 11 \times 2 \\[1em] \Rightarrow y = 22.$

Hence, $\bm{y} = 22$.

Solve :

$\dfrac{z}{7} + 1 = 2\dfrac{1}{2}$

Answer

Solving,

$\Rightarrow \dfrac{z}{7} + 1 = 2\dfrac{1}{2} \\[1em] \Rightarrow \dfrac{z}{7} + 1 = \dfrac{5}{2} \\[1em] \Rightarrow \dfrac{z}{7} = \dfrac{5}{2} - 1 \\[1em] \Rightarrow \dfrac{z}{7} = \dfrac{5 - 2}{2} \\[1em] \Rightarrow \dfrac{z}{7} = \dfrac{3}{2} \\[1em] \Rightarrow z = \dfrac{3}{2} \times 7 \\[1em] \Rightarrow z = \dfrac{21}{2} = 10\dfrac{1}{2}.$

Hence, $\bm{z} = 10\dfrac{1}{2}$.

Solve :

$\dfrac{a}{2.4} - 5 = 2.4$

Answer

Solving,

$\Rightarrow \dfrac{a}{2.4} - 5 = 2.4 \\[1em] \Rightarrow \dfrac{a}{2.4} = 2.4 + 5 \\[1em] \Rightarrow \dfrac{a}{2.4} = 7.4 \\[1em] \Rightarrow a = 7.4 \times 2.4 \\[1em] \Rightarrow a = 17.76.$

Hence, $\bm{a} = 17.76$.

Solve :

$\dfrac{b}{1.6} + 3 = -2.5$

Answer

Solving,

$\Rightarrow \dfrac{b}{1.6} + 3 = -2.5 \\[1em] \Rightarrow \dfrac{b}{1.6} = -2.5 - 3 \\[1em] \Rightarrow \dfrac{b}{1.6} = -5.5 \\[1em] \Rightarrow b = -5.5 \times 1.6 \\[1em] \Rightarrow b = -8.8.$

Hence, $\bm{b} = -8.8$.

Solve :

$\dfrac{m}{4} - 4.6 = -3.1$

Answer

Solving,

$\Rightarrow \dfrac{m}{4} - 4.6 = -3.1 \\[1em] \Rightarrow \dfrac{m}{4} = -3.1 + 4.6 \\[1em] \Rightarrow \dfrac{m}{4} = 1.5 \\[1em] \Rightarrow m = 1.5 \times 4 \\[1em] \Rightarrow m = 6.$

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

Solve :

$-8m - 2 = -10$

Answer

Solving,

$\Rightarrow -8m - 2 = -10 \\[1em] \Rightarrow -8m = -10 + 2 \\[1em] \Rightarrow -8m = -8 \\[1em] \Rightarrow m = \dfrac{-8}{-8} \\[1em] \Rightarrow m = 1.$

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

Solve :

$4x + 2x = 3 + 5$

Answer

Solving,

$\Rightarrow 4x + 2x = 3 + 5 \\[1em] \Rightarrow 6x = 8 \\[1em] \Rightarrow x = \dfrac{8}{6} \\[1em] \Rightarrow x = \dfrac{4}{3} = 1\dfrac{1}{3}.$

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

Solve :

$4x - x + 5 = 8$

Answer

Solving,

$\Rightarrow 4x - x + 5 = 8 \\[1em] \Rightarrow 3x + 5 = 8 \\[1em] \Rightarrow 3x = 8 - 5 \\[1em] \Rightarrow 3x = 3 \\[1em] \Rightarrow x = 1.$

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

Solve :

$6x + 2 = 2x + 10$

Answer

Solving,

$\Rightarrow 6x + 2 = 2x + 10 \\[1em] \Rightarrow 6x - 2x = 10 - 2 \\[1em] \Rightarrow 4x = 8 \\[1em] \Rightarrow x = \dfrac{8}{4} \\[1em] \Rightarrow x = 2.$

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

Solve :

$18 - (2a - 12) = 8a$

Answer

Solving,

$\Rightarrow 18 - (2a - 12) = 8a \\[1em] \Rightarrow 18 - 2a + 12 = 8a \\[1em] \Rightarrow 30 - 2a = 8a \\[1em] \Rightarrow 30 = 8a + 2a \\[1em] \Rightarrow 30 = 10a \\[1em] \Rightarrow a = \dfrac{30}{10} \\[1em] \Rightarrow a = 3.$

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

Solve :

$3x + 5 + 2x + 6 + x = 4x + 21$

Answer

Solving,

$\Rightarrow 3x + 5 + 2x + 6 + x = 4x + 21 \\[1em] \Rightarrow 6x + 11 = 4x + 21 \\[1em] \Rightarrow 6x - 4x = 21 - 11 \\[1em] \Rightarrow 2x = 10 \\[1em] \Rightarrow x = \dfrac{10}{2} \\[1em] \Rightarrow x = 5.$

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

Solve :

$3.5x - 9 - 3 = x + 1$

Answer

Solving,

$\Rightarrow 3.5x - 9 - 3 = x + 1 \\[1em] \Rightarrow 3.5x - 12 = x + 1 \\[1em] \Rightarrow 3.5x - x = 1 + 12 \\[1em] \Rightarrow 2.5x = 13 \\[1em] \Rightarrow x = \dfrac{13}{2.5} \\[1em] \Rightarrow x = \dfrac{26}{5} = 5\dfrac{1}{5}.$

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

Solve :

$8x + 6 + 2x - 4 = 4x + 8$

Answer

Solving,

$\Rightarrow 8x + 6 + 2x - 4 = 4x + 8 \\[1em] \Rightarrow 10x + 2 = 4x + 8 \\[1em] \Rightarrow 10x - 4x = 8 - 2 \\[1em] \Rightarrow 6x = 6 \\[1em] \Rightarrow x = \dfrac{6}{6} \\[1em] \Rightarrow x = 1.$

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

Solve :

$-m + (3m - 6m) = -8 - 14$

Answer

Solving,

$\Rightarrow -m + (3m - 6m) = -8 - 14 \\[1em] \Rightarrow -m + (-3m) = -22 \\[1em] \Rightarrow -m - 3m = -22 \\[1em] \Rightarrow -4m = -22 \\[1em] \Rightarrow m = \dfrac{-22}{-4} \\[1em] \Rightarrow m = \dfrac{11}{2} = 5\dfrac{1}{2}.$

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

Solve :

$5x - 14 = x - (24 + 4x)$

Answer

Solving,

$\Rightarrow 5x - 14 = x - (24 + 4x) \\[1em] \Rightarrow 5x - 14 = x - 24 - 4x \\[1em] \Rightarrow 5x - 14 = -3x - 24 \\[1em] \Rightarrow 5x + 3x = -24 + 14 \\[1em] \Rightarrow 8x = -10 \\[1em] \Rightarrow x = \dfrac{-10}{8} \\[1em] \Rightarrow x = -\dfrac{5}{4} = -1\dfrac{1}{4}.$

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