Question

Solve
$5x + \frac{7}{2} = \frac{3}{2} x - 14$
​

Answer 1

Answer:

5

Step-by-step explanation:

$5x + \frac{7}{2} = \frac{3}{2} x - 14 \\ \frac{7}{2} + 14 = 5x - \frac{3}{2} x \\ \frac{7 + 28}{2} = \frac{10x - 3x}{2} \\ \frac{35}{2} = \frac{7x}{2} \\ \frac{35}{2} \times 2 = 7x \\ 35 = 7x \\ x = \frac{35}{7} = 5$

Answer 2

$\large\frak{\underline{\underline{\red{Solution:-}}}}$

Multiply both sides of the equation by 2:

$\pink{\longrightarrow\:}$ $\sf{\bold{2 \times (5x+\dfrac{7}{2})=2 \times (\dfrac{3}{2}  x-14)}}$

$\pink{\longrightarrow\:}$ $\sf{\bold{(2 \times 5x)+(2 \times \dfrac{7}{2} )=(2 \times \dfrac{3}{2} x)-(2 \times 14)}}$

$\pink{\longrightarrow\:}$ $\sf{\bold{10x-3x=-28-7}}$

$\pink{\longrightarrow\:}$ $\sf{\bold{7x+7=-28}}$

$\pink{\longrightarrow\:}$ $\sf{\bold{7x=-28-7}}$

$\pink{\longrightarrow\:}$ $\sf{\bold{7x=-35}}$

$\pink{\longrightarrow\:}$ $\sf{\bold{x=\dfrac{-35}{7} }}$

$\pink{\longrightarrow\:}$ $\sf{\bold{x=-5}}$

To check :-

❍ L.H.S

$\purple{\longrightarrow\:}$ $\sf{\bold{5x+\dfrac{7}{2} }}$

$\purple{\longrightarrow\:}$ $\sf{\bold{5(-5)+\dfrac{7}{2}  }}$

$\purple{\longrightarrow\:}$ $\sf{\bold{-25+\dfrac{7}{2}   }}$

$\purple{\longrightarrow\:}$ $\sf{\bold{\dfrac{-50+7}{2}  }}$

$\purple{\longrightarrow\:}$ $\sf{\bold{\dfrac{-43}{2}  }}$

❍ R.H.S

$\blue{\longrightarrow\:}$ $\sf{\bold{\dfrac{3x}{2} -14 }}$

$\blue{\longrightarrow\:}$ $\sf{\bold{\dfrac{3(-5)}{2} -14 }}$

$\blue{\longrightarrow\:}$ $\sf{\bold{\dfrac{-15-28}{2} }}$

$\blue{\longrightarrow\:}$ $\sf{\bold{\dfrac{-43}{2} }}$

$\sf{\bold{\therefore LHS = RHS}}$

Hence Verified ! ✔

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