Question

Solve each of the following equation and also verify your solution 5 X upon 3 + 2 upon 5 is equals to 1

Answer 1

Answer:

The solution of the given equation is

$\displaystyle{\boxed{\red{\sf\:x\:=\:\dfrac{9}{25}\:}}}$

Step-by-step-explanation:

The given linear equation is

$\displaystyle{\sf\:\dfrac{5x}{3}\:+\:\dfrac{2}{5}\:=\:1}$

We have to find the value of x.

Now,

$\displaystyle{\sf\:\dfrac{5x}{3}\:+\:\dfrac{2}{5}\:=\:1}$

$\displaystyle{\implies\sf\:\dfrac{5x\:\times\:5\:+\:2\:\times\:3}{3\:\times\:5}\:=\:1}$

$\displaystyle{\implies\sf\:\dfrac{25x\:+\:6}{15}\:=\:1}$

$\displaystyle{\implies\sf\:25x\:+\:6\:=\:1\:\times\:15}$

$\displaystyle{\implies\sf\:25x\:+\:6\:=\:15}$

$\displaystyle{\implies\sf\:25x\:=\:15\:-\:6}$

$\displaystyle{\implies\sf\:25x\:=\:9}$

$\displaystyle{\implies\:\underline{\boxed{\red{\sf\:x\:=\:\dfrac{9}{25}\:}}}}$

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Verification:

The given equation is

$\displaystyle{\sf\:\dfrac{5x}{3}\:+\:\dfrac{2}{5}\:=\:1}$

We have,

$\displaystyle{\sf\:x\:=\:\dfrac{9}{25}}$

By substituting value of x in LHS of given equation, we get,

$\displaystyle{\sf\:\dfrac{5x}{3}\:+\:\dfrac{2}{5}\:=\:1}$

$\displaystyle{\therefore\:\sf\:LHS\:=\:\dfrac{5x}{3}\:+\:\dfrac{2}{5}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\cancel{5}\:\times\:\dfrac{9}{\cancel{25}}}{3}\:+\:\dfrac{2}{5}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{9}{5}}{3}\:+\:\dfrac{2}{5}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{9}{5}\:\times\:\dfrac{1}{3}\:+\:\dfrac{2}{5}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{9}{15}\:+\:\dfrac{2}{5}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{9}{15}\:+\:\dfrac{2}{5}\:\times\:\dfrac{3}{3}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{9}{15}\:+\:\dfrac{6}{15}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{9\:+\:6}{15}}$

$\displaystyle{\implies\sf\:LHS\:=\:\cancel{\dfrac{15}{15}}}$

$\displaystyle{\implies\sf\:LHS\:=\:1}$

$\displaystyle{\sf\:RHS\:=\:1}$

$\displaystyle{\therefore\:\boxed{\red{\sf\:LHS\:=\:RHS\:}}}$

Hence verified!

Answer 2

Given : Linear Equation is

$\rm \frac{5x}{3} + \frac{2}{5} = 1$

Solution :

$\rm⇢ \: \: \frac{5x}{3} + \frac{2}{5} = 1$

$\rm⇢ \: \: \frac{(5x)5 + (2)3 }{3 \times 5} = 1$

$\rm⇢ \: \: \frac{25x + 6}{15} = 1$

$\rm⇢ \: \: 25x + 6 = 15$

$\rm⇢ \: \: 25x = 15 - 6$

$\rm⇢ \: \: 25x = 9$

$\rm⇢ \: \: \boxed{ \orange{ \bf x = \frac{9}{25} }}$

FINAL ANSWER :

The Value of x is 9/25 .