Question

solve the following equation of 2/5=5x-3/2x+1​

Answer 1

Answer:

x=4/7

Step-by-step explanation:

2/5=5x-3/2x+1

2(2x+1)=5(5x-2)

4x+2=25x-10

2+10=25x-4x

12=21x

12/21=x

4/7=x

Answer 2

★ How to do :-

Here, we are given with a fraction and an other fraction which has two same variables x in it. It also has some constants in it. We are said that these two fractions are same. We are asked to find the value of x and then we should verify that whether the obtained fraction equals to the given fraction or not. In verification, if we get both values as equal, then our answer is correct. If we got the result as it's not equal, then the value of x will be wrong. To find the value of x, we make use of an other concept namely the cross multiplication which is always used to compare the fractions. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{2}{5} = \dfrac{5x - 3}{2x + 1}}$

Cross multiply the numbers.

${\tt \leadsto 2 (2x + 1) = 5 (5x - 3)}$

Multiply the numbers outside the bracket with numbers in bracket.

${\tt \leadsto 4x + 2 = 25x - 15}$

Shift the variable value on LHS and the constant value on RHS.

${\tt \leadsto 4x - 25x = - 15 - 2}$

Subtract the values on LHS and RHS.

${\tt \leadsto (- 21x) = (-17)}$

Shift the value (-21) from LHS to RHS.

${\tt \leadsto x = \dfrac{(-17)}{(-21)}}$

Write the obtained fraction in lowest form.

${\tt \leadsto x = \dfrac{17}{21}}$

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${\red{\underline{\boxed{\bf So, \: the \: value \: of \: x \: is \: \dfrac{17}{21}.}}}}$