Question paper, Set 4

$x + 74 = 8$

$\Rightarrow x = 8 - 74$

$\Rightarrow x = -66$

Answer: $x = -66$

$x - 6 = 72$

$\Rightarrow x = 72 + 6$

$\Rightarrow x = 78$

Answer: $x = 78$

$x \times 4 = 312$

$\displaystyle \Rightarrow x = \frac{312}{4}$

$\Rightarrow x = 78$

Answer: $x = 78$

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

$\Rightarrow x = 78 \times 9$

$\Rightarrow x = 702$

Answer: $x = 702$

(i) $x + 82 = -70$

$\Rightarrow x = -70 - 82$

$\Rightarrow x = -152$

(ii) $x - 64 = -57$

$\Rightarrow x = -57 + 64$

$\Rightarrow x = 7$

(iii) $x \times 5 = 195$

$\displaystyle \Rightarrow x = \frac{195}{5}$

$\Rightarrow x = 39$

(iv) $\displaystyle \frac{x}{26} = 834$

$\Rightarrow x = 834 \times 26$

$\Rightarrow x = 21684$

Answer: (i) $x = -152$, (ii) $x = 7$, (iii) $x = 39$, (iv) $x = 21684$

$x - 581 = -803$

$\Rightarrow x = -803 + 581$

Column subtraction: $803 - 581 = 222$; the bigger number is negative, so $x$ is negative

$\Rightarrow x = -222$

Answer: $x = -222$

$x \times 13 = 2665$

$\displaystyle \Rightarrow x = \frac{2665}{13}$

Long division: $26 \div 13 = 2$, remainder $0$; $6 \div 13 = 0$, remainder $6$; $65 \div 13 = 5$, remainder $0$

$\Rightarrow x = 205$

Answer: $x = 205$

$\displaystyle \frac{x}{-3} = 58$

$\Rightarrow x = 58 \times (-3)$

$+ \times - = -$

$\Rightarrow x = -174$

Answer: $x = -174$

$4x - 81 = -185$

$\Rightarrow 4x = -185 + 81$

$\Rightarrow 4x = -104$

$\displaystyle \Rightarrow x = \frac{-104}{4}$

$\Rightarrow x = -26$

Answer: $x = -26$

$\displaystyle \frac{x}{5} - 32 = 65$

$\displaystyle \Rightarrow \frac{x}{5} = 65 + 32$

$\displaystyle \Rightarrow \frac{x}{5} = 97$

$\Rightarrow x = 97 \times 5$

$\Rightarrow x = 485$

Answer: $x = 485$

(i) $\displaystyle \frac{9x}{8} + 24 = -30$

$\displaystyle \Rightarrow \frac{9x}{8} = -30 - 24$

$\displaystyle \Rightarrow \frac{9x}{8} = -54$

$\Rightarrow 9x = -54 \times 8$

$\Rightarrow 9x = -432$

$\displaystyle \Rightarrow x = \frac{-432}{9}$

$\Rightarrow x = -48$

(ii) $\displaystyle \frac{5x}{9} - 37 = -27$

$\displaystyle \Rightarrow \frac{5x}{9} = -27 + 37$

$\displaystyle \Rightarrow \frac{5x}{9} = 10$

$\Rightarrow 5x = 10 \times 9$

$\Rightarrow 5x = 90$

$\displaystyle \Rightarrow x = \frac{90}{5}$

$\Rightarrow x = 18$

Answer: (i) $x = -48$, (ii) $x = 18$

$x + 5 = 45 - x$

$\Rightarrow x + x = 45 - 5$

$\Rightarrow 2x = 40$

$\displaystyle \Rightarrow x = \frac{40}{2}$

$\Rightarrow x = 20$

Answer: $x = 20$

$7x + 25 = 157 - 5x$

$\Rightarrow 7x + 5x = 157 - 25$

$\Rightarrow 12x = 132$

$\displaystyle \Rightarrow x = \frac{132}{12}$

$\Rightarrow x = 11$

Answer: $x = 11$

$4x - 13 + 6x = 17 + 5x$

$\Rightarrow 10x - 13 = 17 + 5x$

$\Rightarrow 10x - 5x = 17 + 13$

$\Rightarrow 5x = 30$

$\displaystyle \Rightarrow x = \frac{30}{5}$

$\Rightarrow x = 6$

Answer: $x = 6$

$60 - 5x = 100$

$\Rightarrow -5x = 100 - 60$

$\Rightarrow -5x = 40$

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

$(+ \div - = -)$

$\Rightarrow x = -8$

Answer: $x = -8$

(i) $3x + 115 = 189 + 5x$

$\Rightarrow 3x - 5x = 189 - 115$

$\Rightarrow -2x = 74$

$\displaystyle \Rightarrow x = \frac{74}{-2}$

$(+ \div - = -)$

$\Rightarrow x = -37$

(ii) $-4x + 30 - 13x = 149$

$\Rightarrow -17x + 30 = 149$

$\Rightarrow -17x = 149 - 30$

$\Rightarrow -17x = 119$

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

$(+ \div - = -)$

$\Rightarrow x = -7$

Answer: (i) $x = -37$, (ii) $x = -7$

Let the other integer be $x$.

$x + (-319) = -898$

$\Rightarrow x = -898 - (-319)$

$\Rightarrow x = -898 + 319$

$\Rightarrow x = -579$

Answer: $-579$

Let the number be $x$.

$229 + x = 194$

$\Rightarrow x = 194 - 229$

$\Rightarrow x = -35$

Answer: $-35$

Let the number be $x$.

$-144 - x = 25$

$\Rightarrow -x = 25 + 144$

$\Rightarrow -x = 169$

$\Rightarrow x = -169$

Answer: $-169$

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

$x \times (-25) = 1925$

$\displaystyle \Rightarrow x = \frac{1925}{-25}$

Long division: $192 \div 25 = 7$, remainder $17$; $175 \div 25 = 7$, remainder $0$

$(+ \div - = -)$

$\Rightarrow x = -77$

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

Larger $-$ smaller $=$ difference

$x - 64 = 33$

$\Rightarrow x = 33 + 64$

$\Rightarrow x = 97$

Answer: (i) $-77$, (ii) $97$