Question paper, Set 10

$x + 17 = -16$

$\Rightarrow x = -16 - 17$

$\Rightarrow x = -33$

Answer: $x = -33$

$x - 95 = 93$

$\Rightarrow x = 93 + 95$

$\Rightarrow x = 188$

Answer: $x = 188$

$6 \times x = 216$

$\displaystyle \Rightarrow x = \frac{216}{6}$

$\Rightarrow x = 36$

Answer: $x = 36$

$\displaystyle \frac{x}{8} = 12$

$\Rightarrow x = 12 \times 8$

$\Rightarrow x = 96$

Answer: $x = 96$

(i) $x + 38 = -57$

$\Rightarrow x = -57 - 38$

$\Rightarrow x = -95$

(ii) $x - 25 = -48$

$\Rightarrow x = -48 + 25$

$\Rightarrow x = -23$

(iii) $4 \times x = 176$

$\displaystyle \Rightarrow x = \frac{176}{4}$

$\Rightarrow x = 44$

(iv) $\displaystyle \frac{x}{28} = 722$

$\Rightarrow x = 722 \times 28$

$\Rightarrow x = 20216$

Answer: (i) $x = -95$, (ii) $x = -23$, (iii) $x = 44$, (iv) $x = 20216$

$x - 336 = -936$

$\Rightarrow x = -936 + 336$

Column subtraction: $936 - 336 = 600$; the bigger number is negative, so $x$ is negative

$\Rightarrow x = -600$

Answer: $x = -600$

$x \times 29 = 23316$

$\displaystyle \Rightarrow x = \frac{23316}{29}$

Long division: $233 \div 29 = 8$, remainder $1$; $11 \div 29 = 0$, remainder $11$; $116 \div 29 = 4$, remainder $0$

$\Rightarrow x = 804$

Answer: $x = 804$

$\displaystyle \frac{x}{-7} = -43$

$\Rightarrow x = (-43) \times (-7)$

$- \times - = +$

$\Rightarrow x = 301$

Answer: $x = 301$

$8x + 32 = 320$

$\Rightarrow 8x = 320 - 32$

$\Rightarrow 8x = 288$

$\displaystyle \Rightarrow x = \frac{288}{8}$

$\Rightarrow x = 36$

Answer: $x = 36$

$\displaystyle \frac{x}{3} + 87 = 160$

$\displaystyle \Rightarrow \frac{x}{3} = 160 - 87$

$\displaystyle \Rightarrow \frac{x}{3} = 73$

$\Rightarrow x = 73 \times 3$

$\Rightarrow x = 219$

Answer: $x = 219$

(i) $\displaystyle \frac{6x}{5} + 20 = -4$

$\displaystyle \Rightarrow \frac{6x}{5} = -4 - 20$

$\displaystyle \Rightarrow \frac{6x}{5} = -24$

$\Rightarrow 6x = -24 \times 5$

$\Rightarrow 6x = -120$

$\displaystyle \Rightarrow x = \frac{-120}{6}$

$\Rightarrow x = -20$

(ii) $\displaystyle \frac{6x}{5} - 40 = -52$

$\displaystyle \Rightarrow \frac{6x}{5} = -52 + 40$

$\displaystyle \Rightarrow \frac{6x}{5} = -12$

$\Rightarrow 6x = -12 \times 5$

$\Rightarrow 6x = -60$

$\displaystyle \Rightarrow x = \frac{-60}{6}$

$\Rightarrow x = -10$

Answer: (i) $x = -20$, (ii) $x = -10$

$x + 37 = 33 - x$

$\Rightarrow x + x = 33 - 37$

$\Rightarrow 2x = -4$

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

$\Rightarrow x = -2$

Answer: $x = -2$

$4x + 2 = -70 - 2x$

$\Rightarrow 4x + 2x = -70 - 2$

$\Rightarrow 6x = -72$

$\displaystyle \Rightarrow x = \frac{-72}{6}$

$\Rightarrow x = -12$

Answer: $x = -12$

$6x + 22 + 3x = -26 + 5x$

$\Rightarrow 9x + 22 = -26 + 5x$

$\Rightarrow 9x - 5x = -26 - 22$

$\Rightarrow 4x = -48$

$\displaystyle \Rightarrow x = \frac{-48}{4}$

$\Rightarrow x = -12$

Answer: $x = -12$

$69 - 7x = 41$

$\Rightarrow -7x = 41 - 69$

$\Rightarrow -7x = -28$

$\displaystyle \Rightarrow x = \frac{-28}{-7}$

$(- \div - = +)$

$\Rightarrow x = 4$

Answer: $x = 4$

(i) $4x + 178 = 55 + 5x$

$\Rightarrow 4x - 5x = 55 - 178$

$\Rightarrow (-1)x = -123$

$\displaystyle \Rightarrow x = \frac{-123}{-1}$

$(- \div - = +)$

$\Rightarrow x = 123$

(ii) $-2x - 17 - 7x = 19$

$\Rightarrow -9x - 17 = 19$

$\Rightarrow -9x = 19 + 17$

$\Rightarrow -9x = 36$

$\displaystyle \Rightarrow x = \frac{36}{-9}$

$(+ \div - = -)$

$\Rightarrow x = -4$

Answer: (i) $x = 123$, (ii) $x = -4$

Let the other integer be $x$.

$x + 213 = -682$

$\Rightarrow x = -682 - 213$

$\Rightarrow x = -895$

Answer: $-895$

Let the number be $x$.

$164 + x = -135$

$\Rightarrow x = -135 - 164$

$\Rightarrow x = -299$

Answer: $-299$

Let the number be $x$.

$-62 - x = 22$

$\Rightarrow -x = 22 + 62$

$\Rightarrow -x = 84$

$\Rightarrow x = -84$

Answer: $-84$

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

$x \times 11 = -506$

$\displaystyle \Rightarrow x = \frac{-506}{11}$

Long division: $50 \div 11 = 4$, remainder $6$; $66 \div 11 = 6$, remainder $0$

$(- \div + = -)$

$\Rightarrow x = -46$

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

Larger $-$ smaller $=$ difference

$x - 59 = 19$

$\Rightarrow x = 19 + 59$

$\Rightarrow x = 78$

Answer: (i) $-46$, (ii) $78$