Simple Equations using Integers: MCQ test, Set 9

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Choose one answer for each question, then check your score at the end. Each correct answer carries 1 mark; there is no negative marking.

If $x + 15 = -12$ , then $x =$
A $27$ B $-27$ C $-3$ D $3$

Answer and solution

Answer: (B) $-27$

$x + 15 = -12$

$\Rightarrow x = -12 - 15$

$\Rightarrow x = -27$
The solution of $x + 76 = 32$ is
A $-108$ B $108$ C $-44$ D $44$

Answer and solution

Answer: (C) $-44$

$x + 76 = 32$

$\Rightarrow x = 32 - 76$

$\Rightarrow x = -44$
Solve $x - 31 = -60$ . Then $x =$
A $91$ B $-91$ C $29$ D $-29$

Answer and solution

Answer: (D) $-29$

$x - 31 = -60$

$\Rightarrow x = -60 + 31$

$\Rightarrow x = -29$
If $x - 5 = 85$ , then $x =$
A $-90$ B $90$ C $80$ D $-80$

Answer and solution

Answer: (B) $90$

$x - 5 = 85$

$\Rightarrow x = 85 + 5$

$\Rightarrow x = 90$
If $x \times 2 = 22$ , then $x =$
A $44$ B $11$ C $110$ D $20$

Answer and solution

Answer: (B) $11$

$x \times 2 = 22$

$\displaystyle \Rightarrow x = \frac{22}{2}$

$\Rightarrow x = 11$
The solution of $\displaystyle \frac{x}{9} = 120$ is
A $1080$ B $129$ C $\displaystyle \frac{40}{3}$ D $111$

Answer and solution

Answer: (A) $1080$

$\displaystyle \frac{x}{9} = 120$

$\Rightarrow x = 120 \times 9$

$\Rightarrow x = 1080$
Which of the following equations has the solution $x = 64$ ?
A $x - 9 = -73$ B $x - 9 = 73$ C $x + 9 = -73$ D $x + 9 = 73$

Answer and solution

Answer: (D) $x + 9 = 73$

Solve each one:

$x + 9 = 73 \Rightarrow x = 73 - 9 = 64$

$x - 9 = 73 \Rightarrow x = 73 + 9 = 82$

$x + 9 = -73 \Rightarrow x = -73 - 9 = -82$

$x - 9 = -73 \Rightarrow x = -73 + 9 = -64$

Only $x + 9 = 73$ gives $x = 64$ .
Which of the following equations has the solution $x = 1053$ ?
A $x \times 9 = 117$ B $x + 9 = 117$ C $\displaystyle \frac{x}{9} = 117$ D $x - 9 = 117$

Answer and solution

Answer: (C) $\displaystyle \frac{x}{9} = 117$

Solve each one:

$x + 9 = 117 \Rightarrow x = 117 - 9 = 108$

$x - 9 = 117 \Rightarrow x = 117 + 9 = 126$

$\displaystyle x \times 9 = 117 \Rightarrow x = \frac{117}{9} = 13$

$\displaystyle \frac{x}{9} = 117 \Rightarrow x = 117 \times 9 = 1053$

Only $\displaystyle \frac{x}{9} = 117$ gives $x = 1053$ .
Solve $x - 286 = -594$ . Then $x =$
A $-312$ B $-308$ C $-880$ D $308$

Answer and solution

Answer: (B) $-308$

$x - 286 = -594$

$\Rightarrow x = -594 + 286$

Column subtraction: $594 - 286 = 308$ ; the bigger number is negative, so $x$ is negative

$\Rightarrow x = -308$
If $x \times 35 = 101535$ , then $x =$
A $29010$ B $291$ C $2910$ D $2901$

Answer and solution

Answer: (D) $2901$

$x \times 35 = 101535$

$\displaystyle \Rightarrow x = \frac{101535}{35}$

Long division: $101 \div 35 = 2$ , remainder $31$ ; $315 \div 35 = 9$ , remainder $0$ ; $3 \div 35 = 0$ , remainder $3$ ; $35 \div 35 = 1$ , remainder $0$

$\Rightarrow x = 2901$
If $\displaystyle \frac{x}{-4} = 87$ , then $x =$
A $-348$ B $\displaystyle -\frac{87}{4}$ C $348$ D $\displaystyle \frac{87}{4}$

Answer and solution

Answer: (A) $-348$

$\displaystyle \frac{x}{-4} = 87$

$\Rightarrow x = 87 \times (-4)$

$+ \times - = -$

$\Rightarrow x = -348$
If $\displaystyle \frac{x}{10} = -163$ , then $x =$
A $\displaystyle \frac{163}{10}$ B $-1630$ C $\displaystyle -\frac{163}{10}$ D $1630$

Answer and solution

Answer: (B) $-1630$

$\displaystyle \frac{x}{10} = -163$

$\Rightarrow x = (-163) \times 10$

$- \times + = -$

$\Rightarrow x = -1630$
The solution of $5x + 111 = -59$ is
A $34$ B $\displaystyle \frac{52}{5}$ C $-34$ D $-170$

Answer and solution

Answer: (C) $-34$

$5x + 111 = -59$

$\Rightarrow 5x = -59 - 111$

$\Rightarrow 5x = -170$

$\displaystyle \Rightarrow x = \frac{-170}{5}$

$\Rightarrow x = -34$
The solution of $9x - 52 = 146$ is
A $\displaystyle \frac{94}{9}$ B $198$ C $-22$ D $22$

Answer and solution

Answer: (D) $22$

$9x - 52 = 146$

$\Rightarrow 9x = 146 + 52$

$\Rightarrow 9x = 198$

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

$\Rightarrow x = 22$
If $\displaystyle \frac{x}{2} + 52 = 77$ , then $x =$
A $\displaystyle \frac{25}{2}$ B $50$ C $258$ D $-50$

Answer and solution

Answer: (B) $50$

$\displaystyle \frac{x}{2} + 52 = 77$

$\displaystyle \Rightarrow \frac{x}{2} = 77 - 52$

$\displaystyle \Rightarrow \frac{x}{2} = 25$

$\Rightarrow x = 25 \times 2$

$\Rightarrow x = 50$
The solution of $\displaystyle \frac{8x}{3} + 5 = -19$ is
A $-9$ B $-72$ C $\displaystyle -\frac{21}{4}$ D $-64$

Answer and solution

Answer: (A) $-9$

$\displaystyle \frac{8x}{3} + 5 = -19$

$\displaystyle \Rightarrow \frac{8x}{3} = -19 - 5$

$\displaystyle \Rightarrow \frac{8x}{3} = -24$

$\Rightarrow 8x = -24 \times 3$

$\Rightarrow 8x = -72$

$\displaystyle \Rightarrow x = \frac{-72}{8}$

$\Rightarrow x = -9$
The solution of $\displaystyle \frac{4x}{9} - 6 = 38$ is
A $\displaystyle \frac{176}{9}$ B $72$ C $99$ D $396$

Answer and solution

Answer: (C) $99$

$\displaystyle \frac{4x}{9} - 6 = 38$

$\displaystyle \Rightarrow \frac{4x}{9} = 38 + 6$

$\displaystyle \Rightarrow \frac{4x}{9} = 44$

$\Rightarrow 4x = 44 \times 9$

$\Rightarrow 4x = 396$

$\displaystyle \Rightarrow x = \frac{396}{4}$

$\Rightarrow x = 99$
If $8x + 13 = 27 - 6x$ , then $x =$
A $1$ B $\displaystyle \frac{20}{7}$ C $-1$ D $7$

Answer and solution

Answer: (A) $1$

$8x + 13 = 27 - 6x$

$\Rightarrow 8x + 6x = 27 - 13$

$\Rightarrow 14x = 14$

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

$\Rightarrow x = 1$
The solution of $3x + 15 + 4x = 19 + 5x$ is
A $-2$ B $\displaystyle \frac{1}{3}$ C $2$ D $17$

Answer and solution

Answer: (C) $2$

$3x + 15 + 4x = 19 + 5x$

$\Rightarrow 7x + 15 = 19 + 5x$

$\Rightarrow 7x - 5x = 19 - 15$

$\Rightarrow 2x = 4$

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

$\Rightarrow x = 2$
Solve $6x - 103 = -49 + 8x$ . Then $x =$
A $76$ B $-27$ C $\displaystyle \frac{27}{7}$ D $27$

Answer and solution

Answer: (B) $-27$

$6x - 103 = -49 + 8x$

$\Rightarrow 6x - 8x = -49 + 103$

$\Rightarrow -2x = 54$

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

$(+ \div - = -)$

$\Rightarrow x = -27$
If $-14x - 13 - 4x = -175$ , then $x =$
A $9$ B $\displaystyle \frac{81}{5}$ C $-9$ D $\displaystyle \frac{94}{9}$

Answer and solution

Answer: (A) $9$

$-14x - 13 - 4x = -175$

$\Rightarrow -18x - 13 = -175$

$\Rightarrow -18x = -175 + 13$

$\Rightarrow -18x = -162$

$\displaystyle \Rightarrow x = \frac{-162}{-18}$

$(- \div - = +)$

$\Rightarrow x = 9$
The sum of two integers is $-910$ . If one of them is $649$ , the other is
A $-261$ B $1559$ C $-1559$ D $261$

Answer and solution

Answer: (C) $-1559$

Let the other integer be $x$ .

$x + 649 = -910$

$\Rightarrow x = -910 - 649$

$\Rightarrow x = -1559$
What number should be added to $-170$ to get $-284$ ?
A $-114$ B $454$ C $114$ D $-454$

Answer and solution

Answer: (A) $-114$

Let the number be $x$ .

$-170 + x = -284$

$\Rightarrow x = -284 - (-170)$

$\Rightarrow x = -284 + 170$

$\Rightarrow x = -114$
What number should be subtracted from $144$ to get $115$ ?
A $-259$ B $-29$ C $259$ D $29$

Answer and solution

Answer: (D) $29$

Let the number be $x$ .

$144 - x = 115$

$\Rightarrow -x = 115 - 144$

$\Rightarrow -x = -29$

$\Rightarrow x = 29$
The product of two integers is $-255$ . If one of them is $15$ , the other is
A $-18$ B $-270$ C $17$ D $-17$

Answer and solution

Answer: (D) $-17$

Let the other integer be $x$ .

$x \times 15 = -255$

$\displaystyle \Rightarrow x = \frac{-255}{15}$

Long division: $25 \div 15 = 1$ , remainder $10$ ; $105 \div 15 = 7$ , remainder $0$

$(- \div + = -)$

$\Rightarrow x = -17$

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MCQ test, Set 9