Tag: solving linear equations

Questions Related to solving linear equations

Solve for $x$:

$\dfrac {9x}{7-6x}=15$

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

  1. $\dfrac{99}{105}$

  2. $-\dfrac{105}{99}$

  3. $\dfrac{105}{99}$

  4. $-\dfrac{99}{105}$

Show answer
Correct Option: C
Explanation:

$\dfrac{9x}{7 - 6x} = 15$


$9x = 15(7 - 6x)  = 105 - 90x$

$9x + 90x = 105 $

$99x = 105$

$x = \dfrac{105}{99}$

If $17x+51y=85$, then $13x+39y=$

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

  1. $67$

  2. $61$

  3. $63$

  4. $65$

Show answer
Correct Option: D
Explanation:

$17x+51y=85$

 dividing both sides by $17$

$\Rightarrow x+3y=5$ 
 on multiplying both sides by $13$
$\Rightarrow 13x+39y=65$
Therefore, $13x+39y=65$

Sabarmati express take 18 second to pass completely through a stations $162$m long and $15 second $ through another station $120m$ long. The length of the sabarmathi express os 

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

  1. $132m$

  2. $100m$

  3. $80m$

  4. $90m$

Show answer
Correct Option: A

The manufacturer of a certain item can sell all he can produce at the selling price of $Rs. 60$ each. It costs him $Rs. 40$ in materials and labour to produce each item and he has overhead expenses of $Rs. 3000$ per week in order to operate the plant. The number of units he should produce and sell in order to make a profit of at least $Rs\,1000$ per week, is : 

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

  1. $200$

  2. $250$

  3. $300$

  4. $400$

Show answer
Correct Option: A
Explanation:

Let the no of units sold be $x$ per week.

$60x$ = sales should include all the expenses and profit required to balance things out.
$60x = 1000+40x+3000$

$20x = 4000$
$x =200$

The value of $x$ for which $\cfrac{x-3}{4}--x< \cfrac{x-1}{2}-\cfrac{x-2}{3}$ and $2-x> 2x-8$

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

  1. $[-1,10/3]$

  2. $(1,10/3)$

  3. $R$

  4. none of these

Show answer
Correct Option: A
Explanation:

$\dfrac{x-3}{4}-x<\dfrac{x-1}{2}-\dfrac{x-2}{3}$


$\dfrac{-3{x}-3}{4}<\dfrac{x+1}{6}$


$\implies x>-1$

$2-x>2{x}-8\implies x<\dfrac{10}{3}$

$\implies x\in (-1,10/3)$

If $\sqrt { 1+\dfrac { x }{ 289 }  } =1\dfrac { 1 }{ 17 }$ then $x=$

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

  1. $1$

  2. $13$

  3. $35$

  4. $15$

Show answer
Correct Option: C
Explanation:

We have,

$\sqrt{1+\dfrac{x}{289}}=1\dfrac{1}{17}$

$\sqrt{\dfrac{289+x}{289}}=\dfrac{18}{17}$

 

On squaring both sides, we get

$ {{\left( \sqrt{\dfrac{289+x}{289}} \right)}^{2}}={{\left( \dfrac{18}{17} \right)}^{2}} $

$ \dfrac{289+x}{289}=\dfrac{324}{289} $

$ 289+x=324 $

$ x=324-289 $

$ x=35 $

 

Hence, this is the answer.

Solve for $x$:-
$\dfrac{{2x - 1}}{2}\,\,\, - \dfrac{{x + 3}}{3}\,\, = \dfrac{{x - 2}}{5}$

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

  1.  $x=\dfrac{5}{14}$

  2.  $x=\dfrac{3}{14}$

  3.  $x=\dfrac{33}{14}$

  4. None of these

Show answer
Correct Option: C
Explanation:

$\dfrac{{2x - 1}}{2}\,\,\, - \dfrac{{x + 3}}{3}\,\, = \dfrac{{x - 2}}{5}\Rightarrow \dfrac{6x-3-2x-6}{6}=\dfrac{x-2}{5}\Rightarrow 20x-45=6x-12\Rightarrow 14x=33\Rightarrow x=\dfrac{33}{14}$

If $\sqrt{10+ \sqrt{25+ \sqrt{x+ \sqrt{154+ \sqrt{225}}}}} = 4$ 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. 110

  2. 108

  3. 100

  4. 114

Show answer
Correct Option: B
Explanation:

We have,

$\sqrt {10+\sqrt {25+\sqrt {x+\sqrt{154+\sqrt{225}}}}}=4$
$\Rightarrow \sqrt {10+\sqrt {25+\sqrt {x+\sqrt{154+15}}}}=4$
$\Rightarrow \sqrt {10+\sqrt {25+\sqrt {x+\sqrt{169}}}}=4$
$\Rightarrow \sqrt {10+\sqrt {25+\sqrt {x+13}}}=4$
On squaring both sides, we get
$10+\sqrt {25+\sqrt {x+13}}=16$
$\sqrt {25+\sqrt {x+13}}=6$
On squaring both sides, we get
$25+\sqrt {x+13}=36$
$\Rightarrow \sqrt {x+13}=11$
On squaring both sides, we get
$x+13=121$
$x=121-13=108$
Hence, $x=108$

If $x(5\, -\, a)\, =\, 10\, -\, x^{2}$ and x = 2, find the value of 'a'.

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

  1. $1$

  2. $8$

  3. $4$

  4. $2$

Show answer
Correct Option: D
Explanation:

$
x(5-a)\quad =\quad 10-{ x }^{ 2 }\ x\quad =\quad 2\ So\ 2(5-a)\quad =\quad 10\quad -{ 2 }^{ 2 }\ 10\quad -\quad 2a\quad =\quad 10-4\ -2a\quad =\quad -4\ a\quad =\quad 2\ 
$

Solve the following equation: 

$(x\, -\, 2)^{2}\, =\, (x\, +\, 1)\, (x\, -\, 1)$

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

  1. $1.5$

  2. $1.75$

  3. $2.25$

  4. $1.25$

Show answer
Correct Option: D
Explanation:

Given, $(x-2)^2=(x+1)(x-1)$

$\Rightarrow x^2-4x+4=x^2-1$ .... Using $(a-b)(a+b)=a^2-b^2$
$\Rightarrow -4x+4=-1$
$\Rightarrow -4x=-5$
$\Rightarrow x=\dfrac {5}{4}=1.25$