Maths M.C.Q. [1 Marks Each]

Given, $\frac{\text{x}}{5}-2=6$
$\Rightarrow \frac{\text{x}}{5}=6+{2}$
$\Rightarrow \frac{\text{x}}{5}={8}$
$\Rightarrow x = 8 \times 5$
$\Rightarrow x = 40$

$\Rightarrow $ Given, $7x - 4 = -25$
$\Rightarrow 7x = -25 + 4$
$\Rightarrow 7x = -21$
$\Rightarrow\text{x} = \frac{-21}{7}$
$\Rightarrow x = -3$

Let the number is $x$
Given, if a number is increased by $25,$ it becomes $40$
$\Rightarrow x + 25 = 40$
$\Rightarrow x = 40 - 25$
$\Rightarrow x = 15$

$3p + 5 = 8$
$\Rightarrow 3p = 8 - 5 = 3$

Let the number is $x$
Given, $10$ less than a number is $55$
$\Rightarrow x - 10 = 55$
$\Rightarrow x = 55 + 10$
$\Rightarrow x = 65$

$3m + 7 = 16$
$\Rightarrow 3m = 16 - 7 = 9$
$\Rightarrow\text{m} =\frac{ 9}{3} = 3$

Given, $\frac{\text{x}}{3} = 4$ then the value of $2x + 5$ is
$\Rightarrow x = 4 \times 3$
$\Rightarrow x = 12$
Now, $2x + 5 = 2 \times 12 + 5 = 24 + 5 = 29$

$4p - 2 = 10$
$\Rightarrow 4p = 10 + 2 = 12$
$\Rightarrow\text{p} = \frac{12}{4} = 3$

Let the number be $x.$
As, twice the number when increased by $7$ gives $25.$
$\Rightarrow 2x + 7 = 25$
$\Rightarrow 2x = 25 - 7 ($By transposing $7$ to $R.H.S.)$
$\Rightarrow 2x = 18$
$\Rightarrow\text{x}=\frac{18}{2} ($By transposing $2$ to $R.H.S.)$
$\therefore\text{x}=9$
So, the number is $9.$
Hence, the correct alternative is option $(b).$

$y + 2 = -2$
$\Rightarrow y = -2 - 2 = -4$

$-4 (2 - x) = 9$
$\Rightarrow -4 \times 2 + 4 \times x = 9$
$\Rightarrow -8 + 4x = 9$
$\Rightarrow 4x = 9 + 8$
$\Rightarrow 4x = 17$
$\Rightarrow\text{x}=\frac{17}{4}$

Let first even number $= 2x$
Then second number $= 2x + 2$
And sum $= 86$
$2x + 2x + 2 - 86$
$\Rightarrow 4x = 86 - 2 = 84$
$\Rightarrow x = 21$
Larger even number $= 2x + 2 = 2 \times 21 + 2 = 42 + 2 = 44$

Let the number $= x$
According to the condition,
$5x = 80 + x$
$⇒ 5x - x = 80$
$⇒ 4x = 80$
$⇒ x = 20$
Number $= 20$

$5\text{x} = 10$
$\Rightarrow\text{x} = \frac{10}{5}$
$= 2$

$8(2x - 5) - 6(3x - 7) = 1$
$⇒ 16x - 40 - 18x + 42 = 1$
$⇒ -2x + 2 = 1$
$⇒ -2x = 1 - 2 = -1$
$\text{x}=\frac{1}{2}$

$x - 6 = 1$
$⇒ x = 1 + 6$
$= 7$

As, $\frac{\text{x}-2}{3}=\frac{2\text{x}-1}{3}-1$
$\Rightarrow\frac{\text{x}-2}{3}-\frac{2\text{x}-1}{3}=-1 ($By transposing $\frac{2\text{x}-1}{3}$ to $L.H.S.)$
$\Rightarrow\frac{(\text{x}-2)-(\text{2x}-1)}{3}=-1$
$\Rightarrow\frac{\text{x}-2-2\text{x}+1}{3}=-1$
$\Rightarrow\frac{-\text{x}-1}{3}=-1$
$\Rightarrow-\text{x}-1=-1\times3( $By transposing $3$ to $R.H.S.)$
$\Rightarrow-\text{x}-1=-3$
$\Rightarrow-\text{x}=-3-1 ($By transposing $-1$ to $R.H.S.)$
$\Rightarrow-\text{x}=-2$
$\therefore\text{x}=2$
Hence, the correct alternative is option $(a).$

In a equation, before equal is called Left-hand side $(LHS)$ and after equal is called Right-hand side $(RHS)$
So in Equation $3x + 4 = 25,$
$RHS$ is $25.$

Let the number be $x.$
According to the equation, we have:
$4x = x + 54$
$\Rightarrow 3x = 54$
$\Rightarrow x = 18$

$3s + 12 = 0$
$\Rightarrow 3s = 0 - 12$
$\Rightarrow 3s = -12$
$\Rightarrow\text{s} = \frac{-12}{3}$
$\Rightarrow s = -4$

As, $2\text{x}-\frac32=\text{5x}+\frac34$
$\Rightarrow2\text{x}-5\text{x}=\frac{3}{4}+\frac{3}{4} ($By transpoing $-\frac32$ to $R.H.S.$ and $5x$ to $L.H.S.)$
$\Rightarrow-3\text{x}=\frac{6}{4}+\frac34$
$\Rightarrow-3\text{x}=\frac{6+3}{4}$
$\Rightarrow\text{x}=\frac{9}{4\times(-3)} ($By transposing $-3$ to $R.H.S.)$
$\Rightarrow\text{x}=\frac{3}{4\times(-1)}$
$\Rightarrow\text{x}=\frac{3}{-4}$
$\therefore\text{x}=-\frac34$
Hence, the correct alternative is option $(b).$

As, $2(2n + 5) = 3(3n - 10)$
$⇒ 4n + 10 = 9n - 30$
$⇒ 4n - 9n = -10 - 30 ($By transposing $10$ to $R.H.S.$ and $9n$ to $L.H.S.)$
$⇒ -5n = -40$
$⇒ n = -40 - 5 ($By transposing $-5$ to $R.H.S.)$
$\therefore\text{n}=8$
Hence, the correct alternative is option $ (d).$

 $\frac{\text{x}}{2}-1=\frac{\text{x}}{3}+4$
$\Rightarrow\frac{\text{x}}{2}-\frac{\text{x}}{3}=4+1$
$\Rightarrow\frac{3\text{x}-2\text{x}}{6}=5$
$\Rightarrow\frac{\text{x}}{6}=5$
$\Rightarrow\text{x}=5\times6=30$
$\therefore\text{x}=30$

$2p - 1 = 3$
$\Rightarrow 2p = 3 + 1 = 4$
$\Rightarrow\text{p} = \frac{4}{2} = 2$