Tag: solving linear equations

Questions Related to solving linear equations

If $3^{2x + 2} = 27^{2}$, find the value of $x$.

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

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: C
Explanation:

Given, $3^{2x+2}=27^{2}$ 

$3^{2x+2}=3^{6}$
Taking $\log$ on both sides give us 
$(2x+2)\log 3=6\log 3$
$\Rightarrow 2x+2=6$ 
$\Rightarrow x=2$

If $2^{x} + 2^{x + 2} = 40$, then the value of $x$ is

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: C
Explanation:

Given, ${ 2 }^{ x }+{ 2 }^{ x+2 }=40\ \Rightarrow { 2 }^{ x }+{ 2 }^{ 2 }{ 2 }^{ x }=40\ \Rightarrow { 2 }^{ x }+(4){ 2 }^{ x }=40\ \Rightarrow (5){ 2 }^{ x }=40\ \Rightarrow { 2 }^{ x }=8\ \Rightarrow { 2 }^{ x }={ 2 }^{ 3 }$

So, $ x=3$

When a number $x$ is subtracted from $36$ and the difference is divided by $x$, the result is $2$. Find the value of $x$.

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

  1. $2$

  2. $4$

  3. $6$

  4. $12$

Show answer
Correct Option: D
Explanation:

According to the question:

$ \dfrac { 36-x }{ x } =2\ \Rightarrow 36-x=2x\ \Rightarrow 36=3x$
$ \Rightarrow x=12$

If $3^{n - 3} + 3^{2} = 18$, calculate the value of $n$.

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

  5. $5$

Show answer
Correct Option: E
Explanation:

Given, ${ 3 }^{ n-3 }+{ 3 }^{ 2 }=18$

$ { 3 }^{ n-3 }+9=18$
${ 3 }^{ n-3 }=18-9=9$
$ { 3 }^{ n-3 }={ 3 }^{ 2 }$
So, $ n-3=2$
$n=5\ $

Let $a, b$ and $c$ be non-zero numbers such that $c$ is $24$ greater than $b$ and $b$ is $24$ greater than $a$. If $\dfrac {c}{a} = 3$, then find the value of $b$.

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

  1. $-48$

  2. $-24$

  3. $24$

  4. $48$

Show answer
Correct Option: D
Explanation:

Let the value of $a$ be $x$

Thus, $b$ would be $24+x$
and $c$ is $24+24+x=48+x$.
Given, $\dfrac {c}{a}=3$
Therefore, $\dfrac {48+x}{x}=3$
$\Rightarrow 2x=48$
$\Rightarrow x=24$
Value of $b$ is $24+x=24+24=48$.

If $\sqrt[3]{8x+6} = -3$, calculate the value of $x$.

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

  1. $-4.125$

  2. $-2.625$

  3. $-1.875$

  4. $-1.125$

Show answer
Correct Option: A
Explanation:

Given $\sqrt [ 3 ]{ 8x+6 } =-3$

Cubing on both sides, we get
$8x+6=(-3)^3$
$\Rightarrow 8x+6=-27\ \Rightarrow x=(-27-6)/8=-33/8\ \Rightarrow x=-4.125$

If $\sqrt[4]{\dfrac{x+1}{2}} = \dfrac{1}{2}$, then find $x $.

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

  1. $-0.969$

  2. $-0.875$

  3. $0$

  4. $0.875$

Show answer
Correct Option: B
Explanation:
Given is $\sqrt [ 4 ]{ \dfrac { x+1 }{ 2 }  } = \dfrac { 1 }{ 2 } $
Now Raising the power to $4$ on both sides, we get
$\dfrac { x+1 }{ 2 } = { \left (\dfrac {1}{2}\right) }^{ 4 }\\ \Rightarrow \dfrac { x+1 }{ 2 } =\dfrac { 1 }{ 16 } \\ \Rightarrow 16x+16=2\\ \Rightarrow x=-0.875$

If $\dfrac{5}{x+3} = \dfrac{1}{x}+\dfrac{1}{2x}$, calculate the value of $x$.

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

  1. $\dfrac{3}{14}$

  2. $\dfrac{1}{3}$

  3. $\dfrac{6}{13}$

  4. $\dfrac{3}{4}$

  5. $\dfrac{9}{7}$

Show answer
Correct Option: E
Explanation:

Given, $\dfrac { 5 }{ x+3 } =\dfrac { 1 }{ x } +\dfrac { 1 }{ 2x } $

Taking RHS:
$\dfrac { 1 }{ x } +\dfrac { 1 }{ 2x } $
LCM of these is $2x$
$\Rightarrow \dfrac { 2 }{ 2x } +\dfrac { 1 }{ 2x } \ \Rightarrow \dfrac { 3 }{ 2x } $
Now taking LHS:
$\dfrac { 5 }{ x+3 } $
It is given, LHS $=$ RHS
$\dfrac { 5 }{ x+3 } =\dfrac { 3 }{ 2x } $
$\Rightarrow 5\times 2x=3\times (x+3)\ \Rightarrow 10x=3x+9\ \Rightarrow x=\dfrac {9}{7}$

One of the requirements for becoming a court reporter is the ability to type  $225$  words per minute. Donald can currently type  $180$  words per minute, and believes that with practice he can increase his typing speed by  $5$  words per minute each month. Which of the following represents the number of words per minute that Donald believes he will be able to type  $m $ months from now?

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

  1. $5 + 180 m$

  2. $ 225 + 5 m$

  3. $ 180 + 5 m$

  4. $ 180 - 5 m$

Show answer
Correct Option: C
Explanation:

With $ m $ months, Donald can type $5m $ more words per  minutes on top of $ 180 $ words.

So, total number of words Donald believes that he will be able to type $ m $ months from now $ = 180 + 5m $

If $\sqrt[3]{5j - 7} = -\cfrac{1}{2}$, calculate the value of $j$.

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

  1. $1.375$

  2. $2.118$

  3. $2.599$

  4. $5.125$

Show answer
Correct Option: A
Explanation:

Given, $\sqrt [ 3 ]{ 5j-7 } =\dfrac { -1 }{ 2 } $

On cubing on both sides, we get
$5j-7=\dfrac { -1 }{ 8 } $
$\Rightarrow 5j=\dfrac { 55 }{ 8 } $
$\Rightarrow j=\dfrac { 11 }{ 8 } $
$\Rightarrow  j = 1.375$
Hence, option A is correct.