Tag: maths

Questions Related to maths

Solve the equation: $\dfrac{x+2}{2x}=1$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $x=2$

  2. $x=3$

  3. $x=4$

  4. $x=5$

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Correct Option: A
Explanation:

Given, $\dfrac{x+2}{2x}=1$
Multiplying both sides by $2x$, we obtain

$x + 2 = 2x$
$2x - x = 2$
$x = 2$

Reduce the following linear equation: $2x + 5 = 3$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $x=1$

  2. $x=-1$

  3. $x=0$

  4. $x=2$

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Correct Option: B
Explanation:

Given, $2x + 5 = 3$
On transposing $5$ to the R.H.S, we obtain 
$2x = 3 - 5$
$2x = -2$
$x = -1$

Calculate the value of $2x+y$, if $\dfrac{1}{2}x=5-\dfrac{1}{4}y$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $20$

  2. $-20$

  3. $10$

  4. $-10$

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Correct Option: A
Explanation:

Given, $\dfrac{1}{2}x=5-\dfrac{1}{4}y$

On multiplying both the sides by $4$, we get
$\Rightarrow 2x=20-y$

Adding $y$ on both the sides,
$\Rightarrow 2x+y=20$

Solve the following equation for the value of $x$: $6\sqrt [ 3 ]{ x } -24=6$.

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $25$

  2. $5$

  3. $100$

  4. $125$

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Correct Option: D
Explanation:

$6\sqrt[3]{x}-24=6$

$\Rightarrow 6\sqrt[3]x=6+24=30$
$\Rightarrow \sqrt[3]x=\dfrac{30}{6}=5$
Taking cube on both sides, we get
$x=5^3=125$

Solve for $x$:
$\dfrac {7}{3x + 4} = \dfrac {7}{6x - 2}$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $-2$

  2. $-1$

  3. $0$

  4. $2$

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Correct Option: D
Explanation:

Given,
$\dfrac { 7 }{ 3x+4 } =\dfrac { 7 }{ 6x-2 } $
$\Rightarrow 42x-14=21x+28$
$\Rightarrow 42x-21x=28+14$
$\Rightarrow 21x=42$
$\Rightarrow x=2$

On a car trip Sam drove  $m$  miles, Kara drove twice as many miles as Sam, and Darin drove  $20$  fewer miles than Kara. In terms of  $m$ , how many miles did Darin drive?

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $2m+20$

  2. $2m-20$

  3. $\frac{m}{2}+20$

  4. $\frac{m+20}{2}$

Show answer
Correct Option: B
Explanation:

Given that

Number of miles driven by $Sam$ $=$ $m$
As $Kara$ drove twice as many miles as $Sam$,
Number of miles drove by $Kara$ $=$ $2m$
As $Darin$ drove 20 fewer miles than $Kara$,

Hence, Number of miles drove by $Darin$ $=$ Number of miles drove by $Kara$ $-$ $20$
$=$ $2m$ $-$ $20$ 
Therfore, $Darin$ drove $'2m$ $-$ $20'$ miles.

If $\dfrac{19}{5x+17} = \dfrac{19}{31}$, then find $x $.

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $0.4$

  2. $1.4$

  3. $2.8$

  4. $3.4$

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Correct Option: C
Explanation:

Given $\dfrac{19}{5x+17} = \dfrac{19}{31}$

$\Rightarrow 19\times 31=19(5x+17)\ \Rightarrow 31=5x+17\ \Rightarrow 5x=14\ \Rightarrow x=\dfrac {14}{5}=2.8$

If $\cfrac{37}{4\sqrt{j}-19} = \cfrac{37}{17}$, then find the value of $j$.

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $64$

  2. $72.25$

  3. $81$

  4. $90.25$

Show answer
Correct Option: C
Explanation:

Given, $\dfrac {{ 37 }}{{ (4\sqrt { j }  }-19)}={ 37 }/{ 17 }$

Since the numerators are equal, we can equate the denominators.
$\Rightarrow { (4\sqrt { j }  }-19)={ 17 }$
$\Rightarrow 4\sqrt { j } =36$
$\Rightarrow \sqrt { j } =9$
So, $j=81$
Hence, option C is correct.

If $\displaystyle \frac{a-b}{b}=\frac{3}{7}$, which of the following must also be true?

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $\displaystyle \frac{a}{b}=-\frac{4}{7}$

  2. $\displaystyle \frac{a}{b}=\frac{10}{7}$

  3. $\displaystyle \frac{a+b}{b}=\frac{10}{7}$

  4. $\displaystyle \frac{a-2b}{b}=-\frac{11}{7}$

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Correct Option: B
Explanation:

Given: $\displaystyle \frac {a-b}{b}=\frac 37$

Separating denominators,

$\Rightarrow \displaystyle \frac ab -1=\frac 37$
$\Rightarrow \displaystyle \frac ab=\frac 37+1=\frac {10}{7}$
$\Rightarrow \dfrac {a}{b}=\dfrac {10}{7}$
Therefore, option B is correct.

If $( 2m) k=6$, then $mk = $

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $3$

  2. $4$

  3. $5$

  4. $6$

Show answer
Correct Option: A
Explanation:

Given, $(2m)k$ $=$ $6$

$\Rightarrow 2$ $\times$ $m$ $\times$ $k$ $=$ $6$
$\Rightarrow m$ $\times$ $k$ $=$ $\dfrac {6}{2}$
$\Rightarrow mk$ $=$ $3$
Therefore, $mk$ $=$ $3$