Simple Equations using Integers: MCQ test, Set 8

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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.

Solve $x + 35 = -15$ . Then $x =$
A $20$ B $-50$ C $50$ D $-20$

Answer and solution

Answer: (B) $-50$

$x + 35 = -15$

$\Rightarrow x = -15 - 35$

$\Rightarrow x = -50$
If $x + 41 = 31$ , then $x =$
A $-72$ B $72$ C $-10$ D $10$

Answer and solution

Answer: (C) $-10$

$x + 41 = 31$

$\Rightarrow x = 31 - 41$

$\Rightarrow x = -10$
If $x - 97 = -31$ , then $x =$
A $-128$ B $128$ C $-66$ D $66$

Answer and solution

Answer: (D) $66$

$x - 97 = -31$

$\Rightarrow x = -31 + 97$

$\Rightarrow x = 66$
If $x - 26 = 5$ , then $x =$
A $31$ B $-21$ C $21$ D $-31$

Answer and solution

Answer: (A) $31$

$x - 26 = 5$

$\Rightarrow x = 5 + 26$

$\Rightarrow x = 31$
If $8 \times x = 368$ , then $x =$
A $460$ B $360$ C $46$ D $2944$

Answer and solution

Answer: (C) $46$

$8 \times x = 368$

$\displaystyle \Rightarrow x = \frac{368}{8}$

$\Rightarrow x = 46$
The solution of $\displaystyle \frac{x}{5} = 44$ is
A $220$ B $49$ C $39$ D $\displaystyle \frac{44}{5}$

Answer and solution

Answer: (A) $220$

$\displaystyle \frac{x}{5} = 44$

$\Rightarrow x = 44 \times 5$

$\Rightarrow x = 220$
Which of the following equations has the solution $x = -50$ ?
A $x - 30 = -80$ B $x + 30 = 80$ C $x - 30 = 80$ D $x + 30 = -80$

Answer and solution

Answer: (A) $x - 30 = -80$

Solve each one:

$x + 30 = 80 \Rightarrow x = 80 - 30 = 50$

$x - 30 = 80 \Rightarrow x = 80 + 30 = 110$

$x + 30 = -80 \Rightarrow x = -80 - 30 = -110$

$x - 30 = -80 \Rightarrow x = -80 + 30 = -50$

Only $x - 30 = -80$ gives $x = -50$ .
Which of the following equations has the solution $x = 1029$ ?
A $x + 7 = 147$ B $\displaystyle \frac{x}{7} = 147$ C $x - 7 = 147$ D $x \times 7 = 147$

Answer and solution

Answer: (B) $\displaystyle \frac{x}{7} = 147$

Solve each one:

$x + 7 = 147 \Rightarrow x = 147 - 7 = 140$

$x - 7 = 147 \Rightarrow x = 147 + 7 = 154$

$\displaystyle x \times 7 = 147 \Rightarrow x = \frac{147}{7} = 21$

$\displaystyle \frac{x}{7} = 147 \Rightarrow x = 147 \times 7 = 1029$

Only $\displaystyle \frac{x}{7} = 147$ gives $x = 1029$ .
The solution of $x + 60851 = 192048$ is
A $-131197$ B $132817$ C $252899$ D $131197$

Answer and solution

Answer: (D) $131197$

$x + 60851 = 192048$

$\Rightarrow x = 192048 - 60851$

Column subtraction: $192048 - 60851 = 131197$

$\Rightarrow x = 131197$
Solve $x \times 34 = 30634$ . Then $x =$
A $910$ B $91$ C $901$ D $9010$

Answer and solution

Answer: (C) $901$

$x \times 34 = 30634$

$\displaystyle \Rightarrow x = \frac{30634}{34}$

Long division: $306 \div 34 = 9$ , remainder $0$ ; $3 \div 34 = 0$ , remainder $3$ ; $34 \div 34 = 1$ , remainder $0$

$\Rightarrow x = 901$
Solve $\displaystyle \frac{x}{-9} = 268$ . Then $x =$
A $\displaystyle -\frac{268}{9}$ B $\displaystyle \frac{268}{9}$ C $-2412$ D $2412$

Answer and solution

Answer: (C) $-2412$

$\displaystyle \frac{x}{-9} = 268$

$\Rightarrow x = 268 \times (-9)$

$+ \times - = -$

$\Rightarrow x = -2412$
Solve $\displaystyle \frac{x}{7} = -147$ . Then $x =$
A $1029$ B $-1029$ C $21$ D $-21$

Answer and solution

Answer: (B) $-1029$

$\displaystyle \frac{x}{7} = -147$

$\Rightarrow x = (-147) \times 7$

$- \times + = -$

$\Rightarrow x = -1029$
The solution of $6x + 118 = 88$ is
A $5$ B $\displaystyle \frac{103}{3}$ C $-30$ D $-5$

Answer and solution

Answer: (D) $-5$

$6x + 118 = 88$

$\Rightarrow 6x = 88 - 118$

$\Rightarrow 6x = -30$

$\displaystyle \Rightarrow x = \frac{-30}{6}$

$\Rightarrow x = -5$
The solution of $2x - 122 = -160$ is
A $-19$ B $19$ C $-141$ D $-38$

Answer and solution

Answer: (A) $-19$

$2x - 122 = -160$

$\Rightarrow 2x = -160 + 122$

$\Rightarrow 2x = -38$

$\displaystyle \Rightarrow x = \frac{-38}{2}$

$\Rightarrow x = -19$
If $\displaystyle \frac{x}{7} + 42 = 26$ , then $x =$
A $112$ B $-112$ C $476$ D $\displaystyle -\frac{16}{7}$

Answer and solution

Answer: (B) $-112$

$\displaystyle \frac{x}{7} + 42 = 26$

$\displaystyle \Rightarrow \frac{x}{7} = 26 - 42$

$\displaystyle \Rightarrow \frac{x}{7} = -16$

$\Rightarrow x = -16 \times 7$

$\Rightarrow x = -112$
If $\displaystyle \frac{4x}{3} + 40 = 88$ , then $x =$
A $96$ B $36$ C $144$ D $64$

Answer and solution

Answer: (B) $36$

$\displaystyle \frac{4x}{3} + 40 = 88$

$\displaystyle \Rightarrow \frac{4x}{3} = 88 - 40$

$\displaystyle \Rightarrow \frac{4x}{3} = 48$

$\Rightarrow 4x = 48 \times 3$

$\Rightarrow 4x = 144$

$\displaystyle \Rightarrow x = \frac{144}{4}$

$\Rightarrow x = 36$
Solve $\displaystyle \frac{3x}{8} - 35 = -59$ . Then $x =$
A $-192$ B $\displaystyle -\frac{752}{3}$ C $-9$ D $-64$

Answer and solution

Answer: (D) $-64$

$\displaystyle \frac{3x}{8} - 35 = -59$

$\displaystyle \Rightarrow \frac{3x}{8} = -59 + 35$

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

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

$\Rightarrow 3x = -192$

$\displaystyle \Rightarrow x = \frac{-192}{3}$

$\Rightarrow x = -64$
The solution of $9x + 35 = 5 - 6x$ is
A $-10$ B $\displaystyle \frac{8}{3}$ C $2$ D $-2$

Answer and solution

Answer: (D) $-2$

$9x + 35 = 5 - 6x$

$\Rightarrow 9x + 6x = 5 - 35$

$\Rightarrow 15x = -30$

$\displaystyle \Rightarrow x = \frac{-30}{15}$

$\Rightarrow x = -2$
If $2x - 6 + 5x = 3 + 4x$ , then $x =$
A $3$ B $-1$ C $\displaystyle -\frac{9}{2}$ D $-3$

Answer and solution

Answer: (A) $3$

$2x - 6 + 5x = 3 + 4x$

$\Rightarrow 7x - 6 = 3 + 4x$

$\Rightarrow 7x - 4x = 3 + 6$

$\Rightarrow 3x = 9$

$\displaystyle \Rightarrow x = \frac{9}{3}$

$\Rightarrow x = 3$
The solution of $3x - 37 = 62 + 6x$ is
A $33$ B $\displaystyle -\frac{25}{3}$ C $11$ D $-33$

Answer and solution

Answer: (D) $-33$

$3x - 37 = 62 + 6x$

$\Rightarrow 3x - 6x = 62 + 37$

$\Rightarrow -3x = 99$

$\displaystyle \Rightarrow x = \frac{99}{-3}$

$(+ \div - = -)$

$\Rightarrow x = -33$
If $77 - 8x = 301$ , then $x =$
A $\displaystyle -\frac{189}{4}$ B $28$ C $-28$ D $224$

Answer and solution

Answer: (C) $-28$

$77 - 8x = 301$

$\Rightarrow -8x = 301 - 77$

$\Rightarrow -8x = 224$

$\displaystyle \Rightarrow x = \frac{224}{-8}$

$(+ \div - = -)$

$\Rightarrow x = -28$
The sum of two integers is $814$ . If one of them is $-830$ , the other is
A $1644$ B $-16$ C $-1644$ D $16$

Answer and solution

Answer: (A) $1644$

Let the other integer be $x$ .

$x + (-830) = 814$

$\Rightarrow x = 814 - (-830)$

$\Rightarrow x = 814 + 830$

$\Rightarrow x = 1644$
What number should be added to $-284$ to get $42$ ?
A $-326$ B $-242$ C $242$ D $326$

Answer and solution

Answer: (D) $326$

Let the number be $x$ .

$-284 + x = 42$

$\Rightarrow x = 42 - (-284)$

$\Rightarrow x = 42 + 284$

$\Rightarrow x = 326$
What number should be subtracted from $-4$ to get $116$ ?
A $-112$ B $-120$ C $120$ D $112$

Answer and solution

Answer: (B) $-120$

Let the number be $x$ .

$-4 - x = 116$

$\Rightarrow -x = 116 + 4$

$\Rightarrow -x = 120$

$\Rightarrow x = -120$
The difference of two integers is $61$ . If the smaller of them is $44$ , the larger is
A $-17$ B $-105$ C $105$ D $17$

Answer and solution

Answer: (C) $105$

Let the larger integer be $x$ .

Larger $-$ smaller $=$ difference

$x - 44 = 61$

$\Rightarrow x = 61 + 44$

$\Rightarrow x = 105$

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MCQ test, Set 8