Question paper, Set 2

$x + 53 = 16$

$\Rightarrow x = 16 - 53$

$\Rightarrow x = -37$

Answer: $x = -37$

$x - 63 = -74$

$\Rightarrow x = -74 + 63$

$\Rightarrow x = -11$

Answer: $x = -11$

$x \times 4 = 320$

$\displaystyle \Rightarrow x = \frac{320}{4}$

$\Rightarrow x = 80$

Answer: $x = 80$

$\displaystyle \frac{x}{5} = 45$

$\Rightarrow x = 45 \times 5$

$\Rightarrow x = 225$

Answer: $x = 225$

(i) $x + 54 = -52$

$\Rightarrow x = -52 - 54$

$\Rightarrow x = -106$

(ii) $x - 84 = -88$

$\Rightarrow x = -88 + 84$

$\Rightarrow x = -4$

(iii) $5 \times x = 185$

$\displaystyle \Rightarrow x = \frac{185}{5}$

$\Rightarrow x = 37$

(iv) $\displaystyle \frac{x}{22} = 130$

$\Rightarrow x = 130 \times 22$

$\Rightarrow x = 2860$

Answer: (i) $x = -106$, (ii) $x = -4$, (iii) $x = 37$, (iv) $x = 2860$

$x - 401 = -597$

$\Rightarrow x = -597 + 401$

Column subtraction: $597 - 401 = 196$; the bigger number is negative, so $x$ is negative

$\Rightarrow x = -196$

Answer: $x = -196$

$x \times 16 = 14512$

$\displaystyle \Rightarrow x = \frac{14512}{16}$

Long division: $145 \div 16 = 9$, remainder $1$; $11 \div 16 = 0$, remainder $11$; $112 \div 16 = 7$, remainder $0$

$\Rightarrow x = 907$

Answer: $x = 907$

$\displaystyle \frac{x}{2} = -66$

$\Rightarrow x = (-66) \times 2$

$- \times + = -$

$\Rightarrow x = -132$

Answer: $x = -132$

$4x + 133 = -3$

$\Rightarrow 4x = -3 - 133$

$\Rightarrow 4x = -136$

$\displaystyle \Rightarrow x = \frac{-136}{4}$

$\Rightarrow x = -34$

Answer: $x = -34$

$\displaystyle \frac{x}{3} + 100 = 90$

$\displaystyle \Rightarrow \frac{x}{3} = 90 - 100$

$\displaystyle \Rightarrow \frac{x}{3} = -10$

$\Rightarrow x = -10 \times 3$

$\Rightarrow x = -30$

Answer: $x = -30$

(i) $\displaystyle \frac{9x}{2} + 3 = 102$

$\displaystyle \Rightarrow \frac{9x}{2} = 102 - 3$

$\displaystyle \Rightarrow \frac{9x}{2} = 99$

$\Rightarrow 9x = 99 \times 2$

$\Rightarrow 9x = 198$

$\displaystyle \Rightarrow x = \frac{198}{9}$

$\Rightarrow x = 22$

(ii) $\displaystyle \frac{8x}{5} - 36 = -92$

$\displaystyle \Rightarrow \frac{8x}{5} = -92 + 36$

$\displaystyle \Rightarrow \frac{8x}{5} = -56$

$\Rightarrow 8x = -56 \times 5$

$\Rightarrow 8x = -280$

$\displaystyle \Rightarrow x = \frac{-280}{8}$

$\Rightarrow x = -35$

Answer: (i) $x = 22$, (ii) $x = -35$

$x + 23 = 49 - x$

$\Rightarrow x + x = 49 - 23$

$\Rightarrow 2x = 26$

$\displaystyle \Rightarrow x = \frac{26}{2}$

$\Rightarrow x = 13$

Answer: $x = 13$

$6x + 3 = 93 - 3x$

$\Rightarrow 6x + 3x = 93 - 3$

$\Rightarrow 9x = 90$

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

$\Rightarrow x = 10$

Answer: $x = 10$

$5x - 23 + 4x = -41 + 7x$

$\Rightarrow 9x - 23 = -41 + 7x$

$\Rightarrow 9x - 7x = -41 + 23$

$\Rightarrow 2x = -18$

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

$\Rightarrow x = -9$

Answer: $x = -9$

$23 - 9x = -103$

$\Rightarrow -9x = -103 - 23$

$\Rightarrow -9x = -126$

$\displaystyle \Rightarrow x = \frac{-126}{-9}$

$(- \div - = +)$

$\Rightarrow x = 14$

Answer: $x = 14$

(i) $3x - 139 = -84 + 4x$

$\Rightarrow 3x - 4x = -84 + 139$

$\Rightarrow (-1)x = 55$

$\displaystyle \Rightarrow x = \frac{55}{-1}$

$(+ \div - = -)$

$\Rightarrow x = -55$

(ii) $-3x + 13 - 6x = 4$

$\Rightarrow -9x + 13 = 4$

$\Rightarrow -9x = 4 - 13$

$\Rightarrow -9x = -9$

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

$(- \div - = +)$

$\Rightarrow x = 1$

Answer: (i) $x = -55$, (ii) $x = 1$

Let the other integer be $x$.

$x + (-121) = -840$

$\Rightarrow x = -840 - (-121)$

$\Rightarrow x = -840 + 121$

$\Rightarrow x = -719$

Answer: $-719$

Let the number be $x$.

$-202 + x = 258$

$\Rightarrow x = 258 - (-202)$

$\Rightarrow x = 258 + 202$

$\Rightarrow x = 460$

Answer: $460$

Let the number be $x$.

$-15 - x = -129$

$\Rightarrow -x = -129 + 15$

$\Rightarrow -x = -114$

$\Rightarrow x = 114$

Answer: $114$

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

$x \times (-12) = -444$

$\displaystyle \Rightarrow x = \frac{-444}{-12}$

Long division: $44 \div 12 = 3$, remainder $8$; $84 \div 12 = 7$, remainder $0$

$(- \div - = +)$

$\Rightarrow x = 37$

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

Larger $-$ smaller $=$ difference

$x - 60 = 81$

$\Rightarrow x = 81 + 60$

$\Rightarrow x = 141$

Answer: (i) $37$, (ii) $141$