Question paper, Set 3

$x + 48 = -41$

$\Rightarrow x = -41 - 48$

$\Rightarrow x = -89$

Answer: $x = -89$

$x - 12 = -64$

$\Rightarrow x = -64 + 12$

$\Rightarrow x = -52$

Answer: $x = -52$

$x \times 4 = 340$

$\displaystyle \Rightarrow x = \frac{340}{4}$

$\Rightarrow x = 85$

Answer: $x = 85$

$\displaystyle \frac{x}{3} = 49$

$\Rightarrow x = 49 \times 3$

$\Rightarrow x = 147$

Answer: $x = 147$

(i) $x + 19 = -51$

$\Rightarrow x = -51 - 19$

$\Rightarrow x = -70$

(ii) $x - 45 = -36$

$\Rightarrow x = -36 + 45$

$\Rightarrow x = 9$

(iii) $x \times 6 = 594$

$\displaystyle \Rightarrow x = \frac{594}{6}$

$\Rightarrow x = 99$

(iv) $\displaystyle \frac{x}{19} = 798$

$\Rightarrow x = 798 \times 19$

$\Rightarrow x = 15162$

Answer: (i) $x = -70$, (ii) $x = 9$, (iii) $x = 99$, (iv) $x = 15162$

$x + 55904 = 154551$

$\Rightarrow x = 154551 - 55904$

Column subtraction: $154551 - 55904 = 98647$

$\Rightarrow x = 98647$

Answer: $x = 98647$

$x \times 22 = 19998$

$\displaystyle \Rightarrow x = \frac{19998}{22}$

Long division: $199 \div 22 = 9$, remainder $1$; $19 \div 22 = 0$, remainder $19$; $198 \div 22 = 9$, remainder $0$

$\Rightarrow x = 909$

Answer: $x = 909$

$\displaystyle \frac{x}{-2} = 31$

$\Rightarrow x = 31 \times (-2)$

$+ \times - = -$

$\Rightarrow x = -62$

Answer: $x = -62$

$5x - 95 = 95$

$\Rightarrow 5x = 95 + 95$

$\Rightarrow 5x = 190$

$\displaystyle \Rightarrow x = \frac{190}{5}$

$\Rightarrow x = 38$

Answer: $x = 38$

$\displaystyle \frac{x}{3} + 25 = 39$

$\displaystyle \Rightarrow \frac{x}{3} = 39 - 25$

$\displaystyle \Rightarrow \frac{x}{3} = 14$

$\Rightarrow x = 14 \times 3$

$\Rightarrow x = 42$

Answer: $x = 42$

(i) $\displaystyle \frac{8x}{9} + 22 = 78$

$\displaystyle \Rightarrow \frac{8x}{9} = 78 - 22$

$\displaystyle \Rightarrow \frac{8x}{9} = 56$

$\Rightarrow 8x = 56 \times 9$

$\Rightarrow 8x = 504$

$\displaystyle \Rightarrow x = \frac{504}{8}$

$\Rightarrow x = 63$

(ii) $\displaystyle \frac{3x}{4} - 24 = -3$

$\displaystyle \Rightarrow \frac{3x}{4} = -3 + 24$

$\displaystyle \Rightarrow \frac{3x}{4} = 21$

$\Rightarrow 3x = 21 \times 4$

$\Rightarrow 3x = 84$

$\displaystyle \Rightarrow x = \frac{84}{3}$

$\Rightarrow x = 28$

Answer: (i) $x = 63$, (ii) $x = 28$

$x + 31 = -23 - x$

$\Rightarrow x + x = -23 - 31$

$\Rightarrow 2x = -54$

$\displaystyle \Rightarrow x = \frac{-54}{2}$

$\Rightarrow x = -27$

Answer: $x = -27$

$6x + 24 = -106 - 7x$

$\Rightarrow 6x + 7x = -106 - 24$

$\Rightarrow 13x = -130$

$\displaystyle \Rightarrow x = \frac{-130}{13}$

$\Rightarrow x = -10$

Answer: $x = -10$

$7x + 30 + 2x = 54 + 6x$

$\Rightarrow 9x + 30 = 54 + 6x$

$\Rightarrow 9x - 6x = 54 - 30$

$\Rightarrow 3x = 24$

$\displaystyle \Rightarrow x = \frac{24}{3}$

$\Rightarrow x = 8$

Answer: $x = 8$

$55 - 6x = 31$

$\Rightarrow -6x = 31 - 55$

$\Rightarrow -6x = -24$

$\displaystyle \Rightarrow x = \frac{-24}{-6}$

$(- \div - = +)$

$\Rightarrow x = 4$

Answer: $x = 4$

(i) $7x - 62 = -86 + 9x$

$\Rightarrow 7x - 9x = -86 + 62$

$\Rightarrow -2x = -24$

$\displaystyle \Rightarrow x = \frac{-24}{-2}$

$(- \div - = +)$

$\Rightarrow x = 12$

(ii) $-12x + 11 - 5x = 130$

$\Rightarrow -17x + 11 = 130$

$\Rightarrow -17x = 130 - 11$

$\Rightarrow -17x = 119$

$\displaystyle \Rightarrow x = \frac{119}{-17}$

$(+ \div - = -)$

$\Rightarrow x = -7$

Answer: (i) $x = 12$, (ii) $x = -7$

Let the other integer be $x$.

$x + 956 = 554$

$\Rightarrow x = 554 - 956$

$\Rightarrow x = -402$

Answer: $-402$

Let the number be $x$.

$112 + x = -152$

$\Rightarrow x = -152 - 112$

$\Rightarrow x = -264$

Answer: $-264$

Let the number be $x$.

$142 - x = 194$

$\Rightarrow -x = 194 - 142$

$\Rightarrow -x = 52$

$\Rightarrow x = -52$

Answer: $-52$

(i) Let the other integer be $x$.

$x \times (-18) = -936$

$\displaystyle \Rightarrow x = \frac{-936}{-18}$

Long division: $93 \div 18 = 5$, remainder $3$; $36 \div 18 = 2$, remainder $0$

$(- \div - = +)$

$\Rightarrow x = 52$

(ii) Let the smaller integer be $x$.

Larger $-$ smaller $=$ difference

$-104 - x = 74$

$\Rightarrow -x = 74 + 104$

$\Rightarrow -x = 178$

$\Rightarrow x = -178$

Answer: (i) $52$, (ii) $-178$