Question

[tex]{\bigstar{\underline{\boxed{\tt{ 5x + \dfrac{7}{2} = \dfrac{3}{5} x - 14 }}}}}[/tex}
The value of the variable x? ​

Answer 1

the value of the variable x is - 5

Step-by-step explanation:

Given :-

${\bigstar{\underline{\boxed{\tt{ 5x + \dfrac{7}{2} = \dfrac{3}{5} x - 14 }}}}}$

To Find :-

The value of the variable x

Solution :-

⋆ Given equation

$\rightarrow \tt \qquad 5x+\dfrac{7}{2} =\dfrac{3}{2}$

⋆ Transposing the terms

$\rightarrow \tt \qquad 5x-\dfrac{3}{2}x =-14 - \dfrac{7}{2}$

⋆ Simplifying it further

$\rightarrow \tt \qquad \dfrac{10x}{2} -\dfrac{3x}{2} =\dfrac{-28}{\;2} - \dfrac{7}{2}$

$\rightarrow \tt \qquad \dfrac{10x - 3x}{2} =\dfrac{-28 -7}{2}$

$\rightarrow \tt \qquad \dfrac{10x - 3x}{2} =\dfrac{-28 -7}{2}$

$\rightarrow \tt \qquad \dfrac{7x}{2} =\dfrac{-35}{\;\;2}$

⋆ Crossmultiplying the fractions

$\rightarrow \tt \qquad 2( 7x ) = 2( - 35 )$

$\rightarrow \tt \qquad 14x = - 70$

$\rightarrow \tt \qquad x =\cancel\dfrac{-70}{\;14}$

$\rightarrow \tt \qquad {\pink{\boxed{\frak{ x = - 5 }}}}$

⋆ Verification :-

$\rightarrow \tt \qquad 5(-5)+\dfrac{7}{2} =\dfrac{3}{2} (-5)-14$

$\rightarrow \tt \qquad - 25+\dfrac{7}{2} =\dfrac{-15}{2} -14$

$\rightarrow \tt \qquad \dfrac{- 50 + 7}{2} =\dfrac{-15-28}{2}$

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Answer 2

Given equation :

5x + 7/2 = 3x/2 – 14

Subtract 7/2both sides of the equation, we get

=> 5x+7/2-7/2=3x/2-14-7/2

=>5x -3x/2=-14 – 7/2

=> (10x-3x)/2 = (-28-7)/2

=> 7x/2 = -35/2

=> x = (-35/2) × (2/7)

=> x = (-35 × 2)/(2×7)

After cancellation, we get

=>x=-5

Therefore,

x= -5