Simple Equations using Integers: MCQ test, Set 10

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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 $x + 42 = -86$ , then $x =$
A $-44$ B $44$ C $128$ D $-128$

Answer and solution

Answer: (D) $-128$

$x + 42 = -86$

$\Rightarrow x = -86 - 42$

$\Rightarrow x = -128$
Solve $x + 46 = 86$ . Then $x =$
A $132$ B $-40$ C $40$ D $-132$

Answer and solution

Answer: (C) $40$

$x + 46 = 86$

$\Rightarrow x = 86 - 46$

$\Rightarrow x = 40$
If $x - 85 = -93$ , then $x =$
A $178$ B $8$ C $-178$ D $-8$

Answer and solution

Answer: (D) $-8$

$x - 85 = -93$

$\Rightarrow x = -93 + 85$

$\Rightarrow x = -8$
The solution of $x - 51 = 31$ is
A $-20$ B $20$ C $82$ D $-82$

Answer and solution

Answer: (C) $82$

$x - 51 = 31$

$\Rightarrow x = 31 + 51$

$\Rightarrow x = 82$
Solve $3 \times x = 267$ . Then $x =$
A $890$ B $264$ C $801$ D $89$

Answer and solution

Answer: (D) $89$

$3 \times x = 267$

$\displaystyle \Rightarrow x = \frac{267}{3}$

$\Rightarrow x = 89$
Solve $\displaystyle \frac{x}{3} = 64$ . Then $x =$
A $192$ B $61$ C $67$ D $\displaystyle \frac{64}{3}$

Answer and solution

Answer: (A) $192$

$\displaystyle \frac{x}{3} = 64$

$\Rightarrow x = 64 \times 3$

$\Rightarrow x = 192$
Which of the following equations has the solution $x = -43$ ?
A $x + 23 = -20$ B $x + 23 = 20$ C $x - 23 = 20$ D $x - 23 = -20$

Answer and solution

Answer: (A) $x + 23 = -20$

Solve each one:

$x + 23 = 20 \Rightarrow x = 20 - 23 = -3$

$x - 23 = 20 \Rightarrow x = 20 + 23 = 43$

$x + 23 = -20 \Rightarrow x = -20 - 23 = -43$

$x - 23 = -20 \Rightarrow x = -20 + 23 = 3$

Only $x + 23 = -20$ gives $x = -43$ .
Which of the following equations has the solution $x = 10$ ?
A $x - 7 = 70$ B $x \times 7 = 70$ C $x + 7 = 70$ D $\displaystyle \frac{x}{7} = 70$

Answer and solution

Answer: (B) $x \times 7 = 70$

Solve each one:

$x + 7 = 70 \Rightarrow x = 70 - 7 = 63$

$x - 7 = 70 \Rightarrow x = 70 + 7 = 77$

$\displaystyle x \times 7 = 70 \Rightarrow x = \frac{70}{7} = 10$

$\displaystyle \frac{x}{7} = 70 \Rightarrow x = 70 \times 7 = 490$

Only $x \times 7 = 70$ gives $x = 10$ .
Solve $x + 28347 = 143851$ . Then $x =$
A $172198$ B $-115504$ C $115504$ D $125516$

Answer and solution

Answer: (C) $115504$

$x + 28347 = 143851$

$\Rightarrow x = 143851 - 28347$

Column subtraction: $143851 - 28347 = 115504$

$\Rightarrow x = 115504$
If $x \times 23 = 139035$ , then $x =$
A $6045$ B $645$ C $60450$ D $6405$

Answer and solution

Answer: (A) $6045$

$x \times 23 = 139035$

$\displaystyle \Rightarrow x = \frac{139035}{23}$

Long division: $139 \div 23 = 6$ , remainder $1$ ; $10 \div 23 = 0$ , remainder $10$ ; $103 \div 23 = 4$ , remainder $11$ ; $115 \div 23 = 5$ , remainder $0$

$\Rightarrow x = 6045$
If $\displaystyle \frac{x}{-7} = 150$ , then $x =$
A $\displaystyle \frac{150}{7}$ B $1050$ C $-1050$ D $\displaystyle -\frac{150}{7}$

Answer and solution

Answer: (C) $-1050$

$\displaystyle \frac{x}{-7} = 150$

$\Rightarrow x = 150 \times (-7)$

$+ \times - = -$

$\Rightarrow x = -1050$
Solve $\displaystyle \frac{x}{2} = -201$ . Then $x =$
A $-402$ B $\displaystyle -\frac{201}{2}$ C $\displaystyle \frac{201}{2}$ D $402$

Answer and solution

Answer: (A) $-402$

$\displaystyle \frac{x}{2} = -201$

$\Rightarrow x = (-201) \times 2$

$- \times + = -$

$\Rightarrow x = -402$
If $7x + 108 = -165$ , then $x =$
A $39$ B $-39$ C $-273$ D $\displaystyle -\frac{57}{7}$

Answer and solution

Answer: (B) $-39$

$7x + 108 = -165$

$\Rightarrow 7x = -165 - 108$

$\Rightarrow 7x = -273$

$\displaystyle \Rightarrow x = \frac{-273}{7}$

$\Rightarrow x = -39$
Solve $2x - 148 = -124$ . Then $x =$
A $24$ B $12$ C $-136$ D $-12$

Answer and solution

Answer: (B) $12$

$2x - 148 = -124$

$\Rightarrow 2x = -124 + 148$

$\Rightarrow 2x = 24$

$\displaystyle \Rightarrow x = \frac{24}{2}$

$\Rightarrow x = 12$
Solve $\displaystyle \frac{x}{3} - 37 = -69$ . Then $x =$
A $96$ B $-318$ C $-96$ D $\displaystyle -\frac{32}{3}$

Answer and solution

Answer: (C) $-96$

$\displaystyle \frac{x}{3} - 37 = -69$

$\displaystyle \Rightarrow \frac{x}{3} = -69 + 37$

$\displaystyle \Rightarrow \frac{x}{3} = -32$

$\Rightarrow x = -32 \times 3$

$\Rightarrow x = -96$
The solution of $\displaystyle \frac{5x}{3} + 38 = 13$ is
A $-15$ B $\displaystyle \frac{153}{5}$ C $-75$ D $\displaystyle -\frac{125}{3}$

Answer and solution

Answer: (A) $-15$

$\displaystyle \frac{5x}{3} + 38 = 13$

$\displaystyle \Rightarrow \frac{5x}{3} = 13 - 38$

$\displaystyle \Rightarrow \frac{5x}{3} = -25$

$\Rightarrow 5x = -25 \times 3$

$\Rightarrow 5x = -75$

$\displaystyle \Rightarrow x = \frac{-75}{5}$

$\Rightarrow x = -15$
Solve $\displaystyle \frac{3x}{8} - 11 = 16$ . Then $x =$
A $\displaystyle \frac{81}{8}$ B $216$ C $\displaystyle \frac{40}{3}$ D $72$

Answer and solution

Answer: (D) $72$

$\displaystyle \frac{3x}{8} - 11 = 16$

$\displaystyle \Rightarrow \frac{3x}{8} = 16 + 11$

$\displaystyle \Rightarrow \frac{3x}{8} = 27$

$\Rightarrow 3x = 27 \times 8$

$\Rightarrow 3x = 216$

$\displaystyle \Rightarrow x = \frac{216}{3}$

$\Rightarrow x = 72$
The solution of $3x - 23 = -63 - 7x$ is
A $10$ B $4$ C $\displaystyle -\frac{43}{5}$ D $-4$

Answer and solution

Answer: (D) $-4$

$3x - 23 = -63 - 7x$

$\Rightarrow 3x + 7x = -63 + 23$

$\Rightarrow 10x = -40$

$\displaystyle \Rightarrow x = \frac{-40}{10}$

$\Rightarrow x = -4$
The solution of $8x + 23 + 3x = -2 + 6x$ is
A $\displaystyle -\frac{25}{2}$ B $5$ C $-5$ D $\displaystyle \frac{21}{5}$

Answer and solution

Answer: (C) $-5$

$8x + 23 + 3x = -2 + 6x$

$\Rightarrow 11x + 23 = -2 + 6x$

$\Rightarrow 11x - 6x = -2 - 23$

$\Rightarrow 5x = -25$

$\displaystyle \Rightarrow x = \frac{-25}{5}$

$\Rightarrow x = -5$
The solution of $4x - 179 = -437 + 5x$ is
A $-258$ B $258$ C $\displaystyle -\frac{86}{3}$ D $616$

Answer and solution

Answer: (B) $258$

$4x - 179 = -437 + 5x$

$\Rightarrow 4x - 5x = -437 + 179$

$\Rightarrow (-1)x = -258$

$\displaystyle \Rightarrow x = \frac{-258}{-1}$

$(- \div - = +)$

$\Rightarrow x = 258$
If $65 - 7x = 170$ , then $x =$
A $-15$ B $\displaystyle -\frac{235}{7}$ C $105$ D $15$

Answer and solution

Answer: (A) $-15$

$65 - 7x = 170$

$\Rightarrow -7x = 170 - 65$

$\Rightarrow -7x = 105$

$\displaystyle \Rightarrow x = \frac{105}{-7}$

$(+ \div - = -)$

$\Rightarrow x = -15$
The sum of two integers is $920$ . If one of them is $963$ , the other is
A $-1883$ B $-43$ C $1883$ D $43$

Answer and solution

Answer: (B) $-43$

Let the other integer be $x$ .

$x + 963 = 920$

$\Rightarrow x = 920 - 963$

$\Rightarrow x = -43$
What number should be added to $160$ to get $-266$ ?
A $-426$ B $106$ C $-106$ D $426$

Answer and solution

Answer: (A) $-426$

Let the number be $x$ .

$160 + x = -266$

$\Rightarrow x = -266 - 160$

$\Rightarrow x = -426$
What number should be subtracted from $114$ to get $43$ ?
A $-71$ B $71$ C $-157$ D $157$

Answer and solution

Answer: (B) $71$

Let the number be $x$ .

$114 - x = 43$

$\Rightarrow -x = 43 - 114$

$\Rightarrow -x = -71$

$\Rightarrow x = 71$
The difference of two integers is $46$ . If the larger of them is $47$ , the smaller is
A $-1$ B $93$ C $-93$ D $1$

Answer and solution

Answer: (D) $1$

Let the smaller integer be $x$ .

Larger $-$ smaller $=$ difference

$47 - x = 46$

$\Rightarrow -x = 46 - 47$

$\Rightarrow -x = -1$

$\Rightarrow x = 1$

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MCQ test, Set 10