Question paper, Set 5

$x + 71 = -34$

$\Rightarrow x = -34 - 71$

$\Rightarrow x = -105$

Answer: $x = -105$

$x - 48 = -8$

$\Rightarrow x = -8 + 48$

$\Rightarrow x = 40$

Answer: $x = 40$

$6 \times x = 198$

$\displaystyle \Rightarrow x = \frac{198}{6}$

$\Rightarrow x = 33$

Answer: $x = 33$

$\displaystyle \frac{x}{3} = 101$

$\Rightarrow x = 101 \times 3$

$\Rightarrow x = 303$

Answer: $x = 303$

(i) $x + 65 = -11$

$\Rightarrow x = -11 - 65$

$\Rightarrow x = -76$

(ii) $x - 35 = -56$

$\Rightarrow x = -56 + 35$

$\Rightarrow x = -21$

(iii) $3 \times x = 213$

$\displaystyle \Rightarrow x = \frac{213}{3}$

$\Rightarrow x = 71$

(iv) $\displaystyle \frac{x}{16} = 820$

$\Rightarrow x = 820 \times 16$

$\Rightarrow x = 13120$

Answer: (i) $x = -76$, (ii) $x = -21$, (iii) $x = 71$, (iv) $x = 13120$

$x + 98539 = 160411$

$\Rightarrow x = 160411 - 98539$

Column subtraction: $160411 - 98539 = 61872$

$\Rightarrow x = 61872$

Answer: $x = 61872$

$x \times 14 = 127204$

$\displaystyle \Rightarrow x = \frac{127204}{14}$

Long division: $127 \div 14 = 9$, remainder $1$; $12 \div 14 = 0$, remainder $12$; $120 \div 14 = 8$, remainder $8$; $84 \div 14 = 6$, remainder $0$

$\Rightarrow x = 9086$

Answer: $x = 9086$

$\displaystyle \frac{x}{-6} = 39$

$\Rightarrow x = 39 \times (-6)$

$+ \times - = -$

$\Rightarrow x = -234$

Answer: $x = -234$

$4x + 97 = 61$

$\Rightarrow 4x = 61 - 97$

$\Rightarrow 4x = -36$

$\displaystyle \Rightarrow x = \frac{-36}{4}$

$\Rightarrow x = -9$

Answer: $x = -9$

$\displaystyle \frac{x}{9} - 23 = 2$

$\displaystyle \Rightarrow \frac{x}{9} = 2 + 23$

$\displaystyle \Rightarrow \frac{x}{9} = 25$

$\Rightarrow x = 25 \times 9$

$\Rightarrow x = 225$

Answer: $x = 225$

(i) $\displaystyle \frac{3x}{2} + 39 = 33$

$\displaystyle \Rightarrow \frac{3x}{2} = 33 - 39$

$\displaystyle \Rightarrow \frac{3x}{2} = -6$

$\Rightarrow 3x = -6 \times 2$

$\Rightarrow 3x = -12$

$\displaystyle \Rightarrow x = \frac{-12}{3}$

$\Rightarrow x = -4$

(ii) $\displaystyle \frac{2x}{9} - 4 = -10$

$\displaystyle \Rightarrow \frac{2x}{9} = -10 + 4$

$\displaystyle \Rightarrow \frac{2x}{9} = -6$

$\Rightarrow 2x = -6 \times 9$

$\Rightarrow 2x = -54$

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

$\Rightarrow x = -27$

Answer: (i) $x = -4$, (ii) $x = -27$

$x + 38 = 32 - x$

$\Rightarrow x + x = 32 - 38$

$\Rightarrow 2x = -6$

$\displaystyle \Rightarrow x = \frac{-6}{2}$

$\Rightarrow x = -3$

Answer: $x = -3$

$2x - 9 = -81 - 7x$

$\Rightarrow 2x + 7x = -81 + 9$

$\Rightarrow 9x = -72$

$\displaystyle \Rightarrow x = \frac{-72}{9}$

$\Rightarrow x = -8$

Answer: $x = -8$

$6x - 7 + 4x = -3 + 8x$

$\Rightarrow 10x - 7 = -3 + 8x$

$\Rightarrow 10x - 8x = -3 + 7$

$\Rightarrow 2x = 4$

$\displaystyle \Rightarrow x = \frac{4}{2}$

$\Rightarrow x = 2$

Answer: $x = 2$

$80 - 7x = -116$

$\Rightarrow -7x = -116 - 80$

$\Rightarrow -7x = -196$

$\displaystyle \Rightarrow x = \frac{-196}{-7}$

$(- \div - = +)$

$\Rightarrow x = 28$

Answer: $x = 28$

(i) $9x - 12 = -92 + 11x$

$\Rightarrow 9x - 11x = -92 + 12$

$\Rightarrow -2x = -80$

$\displaystyle \Rightarrow x = \frac{-80}{-2}$

$(- \div - = +)$

$\Rightarrow x = 40$

(ii) $-4x - 9 - 8x = -21$

$\Rightarrow -12x - 9 = -21$

$\Rightarrow -12x = -21 + 9$

$\Rightarrow -12x = -12$

$\displaystyle \Rightarrow x = \frac{-12}{-12}$

$(- \div - = +)$

$\Rightarrow x = 1$

Answer: (i) $x = 40$, (ii) $x = 1$

Let the other integer be $x$.

$x + 912 = 266$

$\Rightarrow x = 266 - 912$

$\Rightarrow x = -646$

Answer: $-646$

Let the number be $x$.

$-254 + x = 83$

$\Rightarrow x = 83 - (-254)$

$\Rightarrow x = 83 + 254$

$\Rightarrow x = 337$

Answer: $337$

Let the number be $x$.

$-101 - x = 91$

$\Rightarrow -x = 91 + 101$

$\Rightarrow -x = 192$

$\Rightarrow x = -192$

Answer: $-192$

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

$x \times 28 = -1204$

$\displaystyle \Rightarrow x = \frac{-1204}{28}$

Long division: $120 \div 28 = 4$, remainder $8$; $84 \div 28 = 3$, remainder $0$

$(- \div + = -)$

$\Rightarrow x = -43$

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

Larger $-$ smaller $=$ difference

$95 - x = 15$

$\Rightarrow -x = 15 - 95$

$\Rightarrow -x = -80$

$\Rightarrow x = 80$

Answer: (i) $-43$, (ii) $80$