Simple Equations using Integers: MCQ test, Set 4

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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.

The solution of $x + 89 = -50$ is
A $-39$ B $139$ C $39$ D $-139$

Answer and solution

Answer: (D) $-139$

$x + 89 = -50$

$\Rightarrow x = -50 - 89$

$\Rightarrow x = -139$
Solve $x + 7 = 55$ . Then $x =$
A $-48$ B $48$ C $62$ D $-62$

Answer and solution

Answer: (B) $48$

$x + 7 = 55$

$\Rightarrow x = 55 - 7$

$\Rightarrow x = 48$
The solution of $x - 29 = -32$ is
A $-3$ B $61$ C $-61$ D $3$

Answer and solution

Answer: (A) $-3$

$x - 29 = -32$

$\Rightarrow x = -32 + 29$

$\Rightarrow x = -3$
Solve $x - 32 = 3$ . Then $x =$
A $-29$ B $29$ C $35$ D $-35$

Answer and solution

Answer: (C) $35$

$x - 32 = 3$

$\Rightarrow x = 3 + 32$

$\Rightarrow x = 35$
Solve $x \times 6 = 282$ . Then $x =$
A $47$ B $1692$ C $276$ D $470$

Answer and solution

Answer: (A) $47$

$x \times 6 = 282$

$\displaystyle \Rightarrow x = \frac{282}{6}$

$\Rightarrow x = 47$
The solution of $\displaystyle \frac{x}{3} = 137$ is
A $140$ B $\displaystyle \frac{137}{3}$ C $134$ D $411$

Answer and solution

Answer: (D) $411$

$\displaystyle \frac{x}{3} = 137$

$\Rightarrow x = 137 \times 3$

$\Rightarrow x = 411$
Which of the following equations has the solution $x = 1$ ?
A $x - 40 = -39$ B $x + 40 = 39$ C $x + 40 = -39$ D $x - 40 = 39$

Answer and solution

Answer: (A) $x - 40 = -39$

Solve each one:

$x + 40 = 39 \Rightarrow x = 39 - 40 = -1$

$x - 40 = 39 \Rightarrow x = 39 + 40 = 79$

$x + 40 = -39 \Rightarrow x = -39 - 40 = -79$

$x - 40 = -39 \Rightarrow x = -39 + 40 = 1$

Only $x - 40 = -39$ gives $x = 1$ .
Which of the following equations has the solution $x = 30$ ?
A $x - 9 = 270$ B $\displaystyle \frac{x}{9} = 270$ C $x \times 9 = 270$ D $x + 9 = 270$

Answer and solution

Answer: (C) $x \times 9 = 270$

Solve each one:

$x + 9 = 270 \Rightarrow x = 270 - 9 = 261$

$x - 9 = 270 \Rightarrow x = 270 + 9 = 279$

$\displaystyle x \times 9 = 270 \Rightarrow x = \frac{270}{9} = 30$

$\displaystyle \frac{x}{9} = 270 \Rightarrow x = 270 \times 9 = 2430$

Only $x \times 9 = 270$ gives $x = 30$ .
The solution of $x + 70276 = 152021$ is
A $122255$ B $222297$ C $81745$ D $-81745$

Answer and solution

Answer: (C) $81745$

$x + 70276 = 152021$

$\Rightarrow x = 152021 - 70276$

Column subtraction: $152021 - 70276 = 81745$

$\Rightarrow x = 81745$
The solution of $x \times 37 = 150923$ is
A $40790$ B $4079$ C $479$ D $4709$

Answer and solution

Answer: (B) $4079$

$x \times 37 = 150923$

$\displaystyle \Rightarrow x = \frac{150923}{37}$

Long division: $150 \div 37 = 4$ , remainder $2$ ; $29 \div 37 = 0$ , remainder $29$ ; $292 \div 37 = 7$ , remainder $33$ ; $333 \div 37 = 9$ , remainder $0$

$\Rightarrow x = 4079$
The solution of $\displaystyle \frac{x}{-13} = 48$ is
A $\displaystyle \frac{48}{13}$ B $-624$ C $\displaystyle -\frac{48}{13}$ D $624$

Answer and solution

Answer: (B) $-624$

$\displaystyle \frac{x}{-13} = 48$

$\Rightarrow x = 48 \times (-13)$

$+ \times - = -$

$\Rightarrow x = -624$
If $\displaystyle \frac{x}{-11} = -46$ , then $x =$
A $\displaystyle \frac{46}{11}$ B $\displaystyle -\frac{46}{11}$ C $506$ D $-506$

Answer and solution

Answer: (C) $506$

$\displaystyle \frac{x}{-11} = -46$

$\Rightarrow x = (-46) \times (-11)$

$- \times - = +$

$\Rightarrow x = 506$
The solution of $5x + 15 = 90$ is
A $75$ B $-15$ C $15$ D $21$

Answer and solution

Answer: (C) $15$

$5x + 15 = 90$

$\Rightarrow 5x = 90 - 15$

$\Rightarrow 5x = 75$

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

$\Rightarrow x = 15$
If $5x - 11 = -151$ , then $x =$
A $-28$ B $\displaystyle -\frac{162}{5}$ C $-140$ D $28$

Answer and solution

Answer: (A) $-28$

$5x - 11 = -151$

$\Rightarrow 5x = -151 + 11$

$\Rightarrow 5x = -140$

$\displaystyle \Rightarrow x = \frac{-140}{5}$

$\Rightarrow x = -28$
If $\displaystyle \frac{x}{7} + 71 = 46$ , then $x =$
A $-175$ B $819$ C $175$ D $\displaystyle -\frac{25}{7}$

Answer and solution

Answer: (A) $-175$

$\displaystyle \frac{x}{7} + 71 = 46$

$\displaystyle \Rightarrow \frac{x}{7} = 46 - 71$

$\displaystyle \Rightarrow \frac{x}{7} = -25$

$\Rightarrow x = -25 \times 7$

$\Rightarrow x = -175$
Solve $\displaystyle \frac{7x}{8} + 29 = 71$ . Then $x =$
A $\displaystyle \frac{147}{4}$ B $48$ C $336$ D $\displaystyle \frac{800}{7}$

Answer and solution

Answer: (B) $48$

$\displaystyle \frac{7x}{8} + 29 = 71$

$\displaystyle \Rightarrow \frac{7x}{8} = 71 - 29$

$\displaystyle \Rightarrow \frac{7x}{8} = 42$

$\Rightarrow 7x = 42 \times 8$

$\Rightarrow 7x = 336$

$\displaystyle \Rightarrow x = \frac{336}{7}$

$\Rightarrow x = 48$
The solution of $\displaystyle \frac{9x}{8} - 29 = 25$ is
A $48$ B $\displaystyle -\frac{32}{9}$ C $432$ D $\displaystyle \frac{243}{4}$

Answer and solution

Answer: (A) $48$

$\displaystyle \frac{9x}{8} - 29 = 25$

$\displaystyle \Rightarrow \frac{9x}{8} = 25 + 29$

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

$\Rightarrow 9x = 54 \times 8$

$\Rightarrow 9x = 432$

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

$\Rightarrow x = 48$
The solution of $6x - 39 = -75 - 6x$ is
A $3$ B $-36$ C $\displaystyle -\frac{19}{2}$ D $-3$

Answer and solution

Answer: (D) $-3$

$6x - 39 = -75 - 6x$

$\Rightarrow 6x + 6x = -75 + 39$

$\Rightarrow 12x = -36$

$\displaystyle \Rightarrow x = \frac{-36}{12}$

$\Rightarrow x = -3$
The solution of $2x - 16 + 5x = -52 + 3x$ is
A $9$ B $-17$ C $36$ D $-9$

Answer and solution

Answer: (D) $-9$

$2x - 16 + 5x = -52 + 3x$

$\Rightarrow 7x - 16 = -52 + 3x$

$\Rightarrow 7x - 3x = -52 + 16$

$\Rightarrow 4x = -36$

$\displaystyle \Rightarrow x = \frac{-36}{4}$

$\Rightarrow x = -9$
Solve $5x + 120 = 389 + 6x$ . Then $x =$
A $-509$ B $-269$ C $269$ D $\displaystyle \frac{269}{11}$

Answer and solution

Answer: (B) $-269$

$5x + 120 = 389 + 6x$

$\Rightarrow 5x - 6x = 389 - 120$

$\Rightarrow (-1)x = 269$

$\displaystyle \Rightarrow x = \frac{269}{-1}$

$(+ \div - = -)$

$\Rightarrow x = -269$
The solution of $22 - 2x = 14$ is
A $-8$ B $-18$ C $4$ D $-4$

Answer and solution

Answer: (C) $4$

$22 - 2x = 14$

$\Rightarrow -2x = 14 - 22$

$\Rightarrow -2x = -8$

$\displaystyle \Rightarrow x = \frac{-8}{-2}$

$(- \div - = +)$

$\Rightarrow x = 4$
The sum of two integers is $-932$ . If one of them is $-644$ , the other is
A $-1576$ B $1576$ C $-288$ D $288$

Answer and solution

Answer: (C) $-288$

Let the other integer be $x$ .

$x + (-644) = -932$

$\Rightarrow x = -932 - (-644)$

$\Rightarrow x = -932 + 644$

$\Rightarrow x = -288$
What number should be added to $191$ to get $227$ ?
A $-36$ B $418$ C $-418$ D $36$

Answer and solution

Answer: (D) $36$

Let the number be $x$ .

$191 + x = 227$

$\Rightarrow x = 227 - 191$

$\Rightarrow x = 36$
What number should be subtracted from $-26$ to get $-138$ ?
A $-164$ B $112$ C $164$ D $-112$

Answer and solution

Answer: (B) $112$

Let the number be $x$ .

$-26 - x = -138$

$\Rightarrow -x = -138 + 26$

$\Rightarrow -x = -112$

$\Rightarrow x = 112$
The difference of two integers is $88$ . If the smaller of them is $117$ , the larger is
A $-205$ B $29$ C $-29$ D $205$

Answer and solution

Answer: (D) $205$

Let the larger integer be $x$ .

Larger $-$ smaller $=$ difference

$x - 117 = 88$

$\Rightarrow x = 88 + 117$

$\Rightarrow x = 205$

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MCQ test, Set 4