Simple Equations using Integers: MCQ test, Set 2

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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 $x + 63 = -91$ , then $x =$
A $28$ B $-28$ C $-154$ D $154$

Answer and solution

Answer: (C) $-154$

$x + 63 = -91$

$\Rightarrow x = -91 - 63$

$\Rightarrow x = -154$
If $x + 40 = 24$ , then $x =$
A $64$ B $-16$ C $16$ D $-64$

Answer and solution

Answer: (B) $-16$

$x + 40 = 24$

$\Rightarrow x = 24 - 40$

$\Rightarrow x = -16$
Solve $x - 83 = -24$ . Then $x =$
A $59$ B $-107$ C $107$ D $-59$

Answer and solution

Answer: (A) $59$

$x - 83 = -24$

$\Rightarrow x = -24 + 83$

$\Rightarrow x = 59$
The solution of $x - 7 = 62$ is
A $69$ B $55$ C $-55$ D $-69$

Answer and solution

Answer: (A) $69$

$x - 7 = 62$

$\Rightarrow x = 62 + 7$

$\Rightarrow x = 69$
The solution of $x \times 7 = 238$ is
A $340$ B $231$ C $1666$ D $34$

Answer and solution

Answer: (D) $34$

$x \times 7 = 238$

$\displaystyle \Rightarrow x = \frac{238}{7}$

$\Rightarrow x = 34$
The solution of $\displaystyle \frac{x}{5} = 144$ is
A $720$ B $139$ C $149$ D $\displaystyle \frac{144}{5}$

Answer and solution

Answer: (A) $720$

$\displaystyle \frac{x}{5} = 144$

$\Rightarrow x = 144 \times 5$

$\Rightarrow x = 720$
Which of the following equations has the solution $x = 4$ ?
A $x + 4 = -8$ B $x - 4 = 8$ C $x - 4 = -8$ D $x + 4 = 8$

Answer and solution

Answer: (D) $x + 4 = 8$

Solve each one:

$x + 4 = 8 \Rightarrow x = 8 - 4 = 4$

$x - 4 = 8 \Rightarrow x = 8 + 4 = 12$

$x + 4 = -8 \Rightarrow x = -8 - 4 = -12$

$x - 4 = -8 \Rightarrow x = -8 + 4 = -4$

Only $x + 4 = 8$ gives $x = 4$ .
Which of the following equations has the solution $x = 686$ ?
A $\displaystyle \frac{x}{7} = 98$ B $x + 7 = 98$ C $x - 7 = 98$ D $x \times 7 = 98$

Answer and solution

Answer: (A) $\displaystyle \frac{x}{7} = 98$

Solve each one:

$x + 7 = 98 \Rightarrow x = 98 - 7 = 91$

$x - 7 = 98 \Rightarrow x = 98 + 7 = 105$

$\displaystyle x \times 7 = 98 \Rightarrow x = \frac{98}{7} = 14$

$\displaystyle \frac{x}{7} = 98 \Rightarrow x = 98 \times 7 = 686$

Only $\displaystyle \frac{x}{7} = 98$ gives $x = 686$ .
If $x + 28881 = 120504$ , then $x =$
A $108383$ B $-91623$ C $91623$ D $149385$

Answer and solution

Answer: (C) $91623$

$x + 28881 = 120504$

$\Rightarrow x = 120504 - 28881$

Column subtraction: $120504 - 28881 = 91623$

$\Rightarrow x = 91623$
Solve $x \times 33 = 13299$ . Then $x =$
A $430$ B $43$ C $403$ D $4030$

Answer and solution

Answer: (C) $403$

$x \times 33 = 13299$

$\displaystyle \Rightarrow x = \frac{13299}{33}$

Long division: $132 \div 33 = 4$ , remainder $0$ ; $9 \div 33 = 0$ , remainder $9$ ; $99 \div 33 = 3$ , remainder $0$

$\Rightarrow x = 403$
If $\displaystyle \frac{x}{-6} = 179$ , then $x =$
A $\displaystyle -\frac{179}{6}$ B $\displaystyle \frac{179}{6}$ C $1074$ D $-1074$

Answer and solution

Answer: (D) $-1074$

$\displaystyle \frac{x}{-6} = 179$

$\Rightarrow x = 179 \times (-6)$

$+ \times - = -$

$\Rightarrow x = -1074$
Solve $\displaystyle \frac{x}{-9} = -223$ . Then $x =$
A $\displaystyle \frac{223}{9}$ B $2007$ C $\displaystyle -\frac{223}{9}$ D $-2007$

Answer and solution

Answer: (B) $2007$

$\displaystyle \frac{x}{-9} = -223$

$\Rightarrow x = (-223) \times (-9)$

$- \times - = +$

$\Rightarrow x = 2007$
The solution of $4x + 150 = 158$ is
A $77$ B $8$ C $-2$ D $2$

Answer and solution

Answer: (D) $2$

$4x + 150 = 158$

$\Rightarrow 4x = 158 - 150$

$\Rightarrow 4x = 8$

$\displaystyle \Rightarrow x = \frac{8}{4}$

$\Rightarrow x = 2$
The solution of $6x - 67 = 125$ is
A $32$ B $192$ C $\displaystyle \frac{29}{3}$ D $-32$

Answer and solution

Answer: (A) $32$

$6x - 67 = 125$

$\Rightarrow 6x = 125 + 67$

$\Rightarrow 6x = 192$

$\displaystyle \Rightarrow x = \frac{192}{6}$

$\Rightarrow x = 32$
If $\displaystyle \frac{x}{9} + 66 = 44$ , then $x =$
A $990$ B $-198$ C $198$ D $\displaystyle -\frac{22}{9}$

Answer and solution

Answer: (B) $-198$

$\displaystyle \frac{x}{9} + 66 = 44$

$\displaystyle \Rightarrow \frac{x}{9} = 44 - 66$

$\displaystyle \Rightarrow \frac{x}{9} = -22$

$\Rightarrow x = -22 \times 9$

$\Rightarrow x = -198$
Solve $\displaystyle \frac{5x}{2} + 34 = 89$ . Then $x =$
A $\displaystyle \frac{275}{2}$ B $22$ C $110$ D $\displaystyle \frac{246}{5}$

Answer and solution

Answer: (B) $22$

$\displaystyle \frac{5x}{2} + 34 = 89$

$\displaystyle \Rightarrow \frac{5x}{2} = 89 - 34$

$\displaystyle \Rightarrow \frac{5x}{2} = 55$

$\Rightarrow 5x = 55 \times 2$

$\Rightarrow 5x = 110$

$\displaystyle \Rightarrow x = \frac{110}{5}$

$\Rightarrow x = 22$
The solution of $\displaystyle \frac{8x}{9} - 7 = 1$ is
A $\displaystyle \frac{64}{9}$ B $72$ C $\displaystyle -\frac{27}{4}$ D $9$

Answer and solution

Answer: (D) $9$

$\displaystyle \frac{8x}{9} - 7 = 1$

$\displaystyle \Rightarrow \frac{8x}{9} = 1 + 7$

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

$\Rightarrow 8x = 8 \times 9$

$\Rightarrow 8x = 72$

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

$\Rightarrow x = 9$
Solve $9x - 31 = -247 - 9x$ . Then $x =$
A $12$ B $\displaystyle -\frac{139}{9}$ C $-216$ D $-12$

Answer and solution

Answer: (D) $-12$

$9x - 31 = -247 - 9x$

$\Rightarrow 9x + 9x = -247 + 31$

$\Rightarrow 18x = -216$

$\displaystyle \Rightarrow x = \frac{-216}{18}$

$\Rightarrow x = -12$
The solution of $6x - 7 + 8x = 33 + 9x$ is
A $\displaystyle \frac{26}{5}$ B $8$ C $-8$ D $\displaystyle -\frac{40}{3}$

Answer and solution

Answer: (B) $8$

$6x - 7 + 8x = 33 + 9x$

$\Rightarrow 14x - 7 = 33 + 9x$

$\Rightarrow 14x - 9x = 33 + 7$

$\Rightarrow 5x = 40$

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

$\Rightarrow x = 8$
If $5x + 131 = 52 + 6x$ , then $x =$
A $79$ B $-183$ C $\displaystyle -\frac{79}{11}$ D $-79$

Answer and solution

Answer: (A) $79$

$5x + 131 = 52 + 6x$

$\Rightarrow 5x - 6x = 52 - 131$

$\Rightarrow (-1)x = -79$

$\displaystyle \Rightarrow x = \frac{-79}{-1}$

$(- \div - = +)$

$\Rightarrow x = 79$
The solution of $42 - 5x = 32$ is
A $-2$ B $\displaystyle -\frac{74}{5}$ C $2$ D $-10$

Answer and solution

Answer: (C) $2$

$42 - 5x = 32$

$\Rightarrow -5x = 32 - 42$

$\Rightarrow -5x = -10$

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

$(- \div - = +)$

$\Rightarrow x = 2$
The sum of two integers is $-198$ . If one of them is $-894$ , the other is
A $-1092$ B $696$ C $-696$ D $1092$

Answer and solution

Answer: (B) $696$

Let the other integer be $x$ .

$x + (-894) = -198$

$\Rightarrow x = -198 - (-894)$

$\Rightarrow x = -198 + 894$

$\Rightarrow x = 696$
What number should be added to $257$ to get $-274$ ?
A $-17$ B $17$ C $-531$ D $531$

Answer and solution

Answer: (C) $-531$

Let the number be $x$ .

$257 + x = -274$

$\Rightarrow x = -274 - 257$

$\Rightarrow x = -531$
What number should be subtracted from $15$ to get $4$ ?
A $19$ B $-19$ C $11$ D $-11$

Answer and solution

Answer: (C) $11$

Let the number be $x$ .

$15 - x = 4$

$\Rightarrow -x = 4 - 15$

$\Rightarrow -x = -11$

$\Rightarrow x = 11$
The difference of two integers is $87$ . If the larger of them is $-84$ , the smaller is
A $3$ B $-3$ C $171$ D $-171$

Answer and solution

Answer: (D) $-171$

Let the smaller integer be $x$ .

Larger $-$ smaller $=$ difference

$-84 - x = 87$

$\Rightarrow -x = 87 + 84$

$\Rightarrow -x = 171$

$\Rightarrow x = -171$

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MCQ test, Set 2