Simple Equations using Integers: MCQ test, Set 3

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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 $x + 21 = -2$ is
A $-19$ B $23$ C $19$ D $-23$

Answer and solution

Answer: (D) $-23$

$x + 21 = -2$

$\Rightarrow x = -2 - 21$

$\Rightarrow x = -23$
The solution of $x + 61 = 94$ is
A $-33$ B $-155$ C $33$ D $155$

Answer and solution

Answer: (C) $33$

$x + 61 = 94$

$\Rightarrow x = 94 - 61$

$\Rightarrow x = 33$
The solution of $x - 72 = -55$ is
A $-17$ B $127$ C $-127$ D $17$

Answer and solution

Answer: (D) $17$

$x - 72 = -55$

$\Rightarrow x = -55 + 72$

$\Rightarrow x = 17$
If $x - 92 = 57$ , then $x =$
A $-149$ B $35$ C $149$ D $-35$

Answer and solution

Answer: (C) $149$

$x - 92 = 57$

$\Rightarrow x = 57 + 92$

$\Rightarrow x = 149$
Solve $x \times 7 = 364$ . Then $x =$
A $52$ B $520$ C $357$ D $2548$

Answer and solution

Answer: (A) $52$

$x \times 7 = 364$

$\displaystyle \Rightarrow x = \frac{364}{7}$

$\Rightarrow x = 52$
The solution of $\displaystyle \frac{x}{4} = 94$ is
A $\displaystyle \frac{47}{2}$ B $376$ C $90$ D $98$

Answer and solution

Answer: (B) $376$

$\displaystyle \frac{x}{4} = 94$

$\Rightarrow x = 94 \times 4$

$\Rightarrow x = 376$
Which of the following equations has the solution $x = 63$ ?
A $x - 18 = -45$ B $x + 18 = -45$ C $x + 18 = 45$ D $x - 18 = 45$

Answer and solution

Answer: (D) $x - 18 = 45$

Solve each one:

$x + 18 = 45 \Rightarrow x = 45 - 18 = 27$

$x - 18 = 45 \Rightarrow x = 45 + 18 = 63$

$x + 18 = -45 \Rightarrow x = -45 - 18 = -63$

$x - 18 = -45 \Rightarrow x = -45 + 18 = -27$

Only $x - 18 = 45$ gives $x = 63$ .
Which of the following equations has the solution $x = 21$ ?
A $\displaystyle \frac{x}{6} = 126$ B $x \times 6 = 126$ C $x + 6 = 126$ D $x - 6 = 126$

Answer and solution

Answer: (B) $x \times 6 = 126$

Solve each one:

$x + 6 = 126 \Rightarrow x = 126 - 6 = 120$

$x - 6 = 126 \Rightarrow x = 126 + 6 = 132$

$\displaystyle x \times 6 = 126 \Rightarrow x = \frac{126}{6} = 21$

$\displaystyle \frac{x}{6} = 126 \Rightarrow x = 126 \times 6 = 756$

Only $x \times 6 = 126$ gives $x = 21$ .
Solve $x - 565 = -822$ . Then $x =$
A $-1387$ B $257$ C $-257$ D $-343$

Answer and solution

Answer: (C) $-257$

$x - 565 = -822$

$\Rightarrow x = -822 + 565$

Column subtraction: $822 - 565 = 257$ ; the bigger number is negative, so $x$ is negative

$\Rightarrow x = -257$
If $x \times 19 = 7619$ , then $x =$
A $41$ B $4010$ C $410$ D $401$

Answer and solution

Answer: (D) $401$

$x \times 19 = 7619$

$\displaystyle \Rightarrow x = \frac{7619}{19}$

Long division: $76 \div 19 = 4$ , remainder $0$ ; $1 \div 19 = 0$ , remainder $1$ ; $19 \div 19 = 1$ , remainder $0$

$\Rightarrow x = 401$
The solution of $\displaystyle \frac{x}{-3} = 119$ is
A $-357$ B $\displaystyle -\frac{119}{3}$ C $\displaystyle \frac{119}{3}$ D $357$

Answer and solution

Answer: (A) $-357$

$\displaystyle \frac{x}{-3} = 119$

$\Rightarrow x = 119 \times (-3)$

$+ \times - = -$

$\Rightarrow x = -357$
Solve $\displaystyle \frac{x}{4} = -198$ . Then $x =$
A $-792$ B $\displaystyle -\frac{99}{2}$ C $792$ D $\displaystyle \frac{99}{2}$

Answer and solution

Answer: (A) $-792$

$\displaystyle \frac{x}{4} = -198$

$\Rightarrow x = (-198) \times 4$

$- \times + = -$

$\Rightarrow x = -792$
Solve $5x + 84 = 164$ . Then $x =$
A $-16$ B $16$ C $\displaystyle \frac{248}{5}$ D $80$

Answer and solution

Answer: (B) $16$

$5x + 84 = 164$

$\Rightarrow 5x = 164 - 84$

$\Rightarrow 5x = 80$

$\displaystyle \Rightarrow x = \frac{80}{5}$

$\Rightarrow x = 16$
Solve $7x - 125 = 57$ . Then $x =$
A $26$ B $-26$ C $\displaystyle -\frac{68}{7}$ D $182$

Answer and solution

Answer: (A) $26$

$7x - 125 = 57$

$\Rightarrow 7x = 57 + 125$

$\Rightarrow 7x = 182$

$\displaystyle \Rightarrow x = \frac{182}{7}$

$\Rightarrow x = 26$
The solution of $\displaystyle \frac{x}{9} - 130 = -31$ is
A $891$ B $-891$ C $11$ D $-1449$

Answer and solution

Answer: (A) $891$

$\displaystyle \frac{x}{9} - 130 = -31$

$\displaystyle \Rightarrow \frac{x}{9} = -31 + 130$

$\displaystyle \Rightarrow \frac{x}{9} = 99$

$\Rightarrow x = 99 \times 9$

$\Rightarrow x = 891$
Solve $\displaystyle \frac{8x}{5} + 18 = -46$ . Then $x =$
A $\displaystyle -\frac{35}{2}$ B $-320$ C $-40$ D $\displaystyle -\frac{512}{5}$

Answer and solution

Answer: (C) $-40$

$\displaystyle \frac{8x}{5} + 18 = -46$

$\displaystyle \Rightarrow \frac{8x}{5} = -46 - 18$

$\displaystyle \Rightarrow \frac{8x}{5} = -64$

$\Rightarrow 8x = -64 \times 5$

$\Rightarrow 8x = -320$

$\displaystyle \Rightarrow x = \frac{-320}{8}$

$\Rightarrow x = -40$
Solve $\displaystyle \frac{4x}{5} - 39 = -31$ . Then $x =$
A $40$ B $\displaystyle \frac{32}{5}$ C $\displaystyle -\frac{175}{2}$ D $10$

Answer and solution

Answer: (D) $10$

$\displaystyle \frac{4x}{5} - 39 = -31$

$\displaystyle \Rightarrow \frac{4x}{5} = -31 + 39$

$\displaystyle \Rightarrow \frac{4x}{5} = 8$

$\Rightarrow 4x = 8 \times 5$

$\Rightarrow 4x = 40$

$\displaystyle \Rightarrow x = \frac{40}{4}$

$\Rightarrow x = 10$
If $8x - 36 = 39 - 7x$ , then $x =$
A $5$ B $-5$ C $75$ D $\displaystyle \frac{1}{5}$

Answer and solution

Answer: (A) $5$

$8x - 36 = 39 - 7x$

$\Rightarrow 8x + 7x = 39 + 36$

$\Rightarrow 15x = 75$

$\displaystyle \Rightarrow x = \frac{75}{15}$

$\Rightarrow x = 5$
The solution of $9x - 27 + 6x = -49 + 13x$ is
A $\displaystyle \frac{11}{2}$ B $-11$ C $11$ D $-38$

Answer and solution

Answer: (B) $-11$

$9x - 27 + 6x = -49 + 13x$

$\Rightarrow 15x - 27 = -49 + 13x$

$\Rightarrow 15x - 13x = -49 + 27$

$\Rightarrow 2x = -22$

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

$\Rightarrow x = -11$
The solution of $3x - 81 = -285 + 4x$ is
A $\displaystyle -\frac{204}{7}$ B $204$ C $-204$ D $366$

Answer and solution

Answer: (B) $204$

$3x - 81 = -285 + 4x$

$\Rightarrow 3x - 4x = -285 + 81$

$\Rightarrow (-1)x = -204$

$\displaystyle \Rightarrow x = \frac{-204}{-1}$

$(- \div - = +)$

$\Rightarrow x = 204$
Solve $-8x - 2 - 10x = 34$ . Then $x =$
A $18$ B $\displaystyle -\frac{16}{9}$ C $-2$ D $2$

Answer and solution

Answer: (C) $-2$

$-8x - 2 - 10x = 34$

$\Rightarrow -18x - 2 = 34$

$\Rightarrow -18x = 34 + 2$

$\Rightarrow -18x = 36$

$\displaystyle \Rightarrow x = \frac{36}{-18}$

$(+ \div - = -)$

$\Rightarrow x = -2$
The sum of two integers is $107$ . If one of them is $414$ , the other is
A $521$ B $-307$ C $307$ D $-521$

Answer and solution

Answer: (B) $-307$

Let the other integer be $x$ .

$x + 414 = 107$

$\Rightarrow x = 107 - 414$

$\Rightarrow x = -307$
What number should be added to $-58$ to get $-290$ ?
A $232$ B $348$ C $-348$ D $-232$

Answer and solution

Answer: (D) $-232$

Let the number be $x$ .

$-58 + x = -290$

$\Rightarrow x = -290 - (-58)$

$\Rightarrow x = -290 + 58$

$\Rightarrow x = -232$
What number should be subtracted from $138$ to get $103$ ?
A $-35$ B $241$ C $35$ D $-241$

Answer and solution

Answer: (C) $35$

Let the number be $x$ .

$138 - x = 103$

$\Rightarrow -x = 103 - 138$

$\Rightarrow -x = -35$

$\Rightarrow x = 35$
The product of two integers is $-644$ . If one of them is $23$ , the other is
A $-28$ B $-667$ C $28$ D $-29$

Answer and solution

Answer: (A) $-28$

Let the other integer be $x$ .

$x \times 23 = -644$

$\displaystyle \Rightarrow x = \frac{-644}{23}$

Long division: $64 \div 23 = 2$ , remainder $18$ ; $184 \div 23 = 8$ , remainder $0$

$(- \div + = -)$

$\Rightarrow x = -28$

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MCQ test, Set 3