Question paper, Set 8

$x + 49 = 52$

$\Rightarrow x = 52 - 49$

$\Rightarrow x = 3$

Answer: $x = 3$

$x - 67 = 29$

$\Rightarrow x = 29 + 67$

$\Rightarrow x = 96$

Answer: $x = 96$

$x \times 7 = 616$

$\displaystyle \Rightarrow x = \frac{616}{7}$

$\Rightarrow x = 88$

Answer: $x = 88$

$\displaystyle \frac{x}{7} = 109$

$\Rightarrow x = 109 \times 7$

$\Rightarrow x = 763$

Answer: $x = 763$

(i) $x + 73 = -10$

$\Rightarrow x = -10 - 73$

$\Rightarrow x = -83$

(ii) $x - 11 = -14$

$\Rightarrow x = -14 + 11$

$\Rightarrow x = -3$

(iii) $x \times 3 = 123$

$\displaystyle \Rightarrow x = \frac{123}{3}$

$\Rightarrow x = 41$

(iv) $\displaystyle \frac{x}{29} = 420$

$\Rightarrow x = 420 \times 29$

$\Rightarrow x = 12180$

Answer: (i) $x = -83$, (ii) $x = -3$, (iii) $x = 41$, (iv) $x = 12180$

$x - 118 = -603$

$\Rightarrow x = -603 + 118$

Column subtraction: $603 - 118 = 485$; the bigger number is negative, so $x$ is negative

$\Rightarrow x = -485$

Answer: $x = -485$

$x \times 17 = 120275$

$\displaystyle \Rightarrow x = \frac{120275}{17}$

Long division: $120 \div 17 = 7$, remainder $1$; $12 \div 17 = 0$, remainder $12$; $127 \div 17 = 7$, remainder $8$; $85 \div 17 = 5$, remainder $0$

$\Rightarrow x = 7075$

Answer: $x = 7075$

$\displaystyle \frac{x}{-9} = -78$

$\Rightarrow x = (-78) \times (-9)$

$- \times - = +$

$\Rightarrow x = 702$

Answer: $x = 702$

$7x - 46 = -277$

$\Rightarrow 7x = -277 + 46$

$\Rightarrow 7x = -231$

$\displaystyle \Rightarrow x = \frac{-231}{7}$

$\Rightarrow x = -33$

Answer: $x = -33$

$\displaystyle \frac{x}{7} - 124 = -171$

$\displaystyle \Rightarrow \frac{x}{7} = -171 + 124$

$\displaystyle \Rightarrow \frac{x}{7} = -47$

$\Rightarrow x = -47 \times 7$

$\Rightarrow x = -329$

Answer: $x = -329$

(i) $\displaystyle \frac{2x}{7} + 5 = -13$

$\displaystyle \Rightarrow \frac{2x}{7} = -13 - 5$

$\displaystyle \Rightarrow \frac{2x}{7} = -18$

$\Rightarrow 2x = -18 \times 7$

$\Rightarrow 2x = -126$

$\displaystyle \Rightarrow x = \frac{-126}{2}$

$\Rightarrow x = -63$

(ii) $\displaystyle \frac{8x}{5} - 13 = -53$

$\displaystyle \Rightarrow \frac{8x}{5} = -53 + 13$

$\displaystyle \Rightarrow \frac{8x}{5} = -40$

$\Rightarrow 8x = -40 \times 5$

$\Rightarrow 8x = -200$

$\displaystyle \Rightarrow x = \frac{-200}{8}$

$\Rightarrow x = -25$

Answer: (i) $x = -63$, (ii) $x = -25$

$x + 40 = -20 - x$

$\Rightarrow x + x = -20 - 40$

$\Rightarrow 2x = -60$

$\displaystyle \Rightarrow x = \frac{-60}{2}$

$\Rightarrow x = -30$

Answer: $x = -30$

$2x - 28 = 62 - 7x$

$\Rightarrow 2x + 7x = 62 + 28$

$\Rightarrow 9x = 90$

$\displaystyle \Rightarrow x = \frac{90}{9}$

$\Rightarrow x = 10$

Answer: $x = 10$

$8x - 24 + 3x = 24 + 5x$

$\Rightarrow 11x - 24 = 24 + 5x$

$\Rightarrow 11x - 5x = 24 + 24$

$\Rightarrow 6x = 48$

$\displaystyle \Rightarrow x = \frac{48}{6}$

$\Rightarrow x = 8$

Answer: $x = 8$

$21 - 3x = -9$

$\Rightarrow -3x = -9 - 21$

$\Rightarrow -3x = -30$

$\displaystyle \Rightarrow x = \frac{-30}{-3}$

$(- \div - = +)$

$\Rightarrow x = 10$

Answer: $x = 10$

(i) $10x + 153 = 45 + 13x$

$\Rightarrow 10x - 13x = 45 - 153$

$\Rightarrow -3x = -108$

$\displaystyle \Rightarrow x = \frac{-108}{-3}$

$(- \div - = +)$

$\Rightarrow x = 36$

(ii) $-4x + 12 - 5x = -51$

$\Rightarrow -9x + 12 = -51$

$\Rightarrow -9x = -51 - 12$

$\Rightarrow -9x = -63$

$\displaystyle \Rightarrow x = \frac{-63}{-9}$

$(- \div - = +)$

$\Rightarrow x = 7$

Answer: (i) $x = 36$, (ii) $x = 7$

Let the other integer be $x$.

$x + 42 = 176$

$\Rightarrow x = 176 - 42$

$\Rightarrow x = 134$

Answer: $134$

Let the number be $x$.

$104 + x = 186$

$\Rightarrow x = 186 - 104$

$\Rightarrow x = 82$

Answer: $82$

Let the number be $x$.

$-130 - x = -127$

$\Rightarrow -x = -127 + 130$

$\Rightarrow -x = 3$

$\Rightarrow x = -3$

Answer: $-3$

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

$x \times 19 = -1235$

$\displaystyle \Rightarrow x = \frac{-1235}{19}$

Long division: $123 \div 19 = 6$, remainder $9$; $95 \div 19 = 5$, remainder $0$

$(- \div + = -)$

$\Rightarrow x = -65$

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

Larger $-$ smaller $=$ difference

$x - (-18) = 78$

$\Rightarrow x = 78 + (-18)$

$\Rightarrow x = 60$

Answer: (i) $-65$, (ii) $60$