Question

.Sollution of the equation :4/x -3 =5/(2x +3) are : *​

Answer 1

Step-by-step explanation:

4/x -3 =5/(2x +3)

Cross-multiply

5(x-3) = 4(2x+3)

5x - 15 = 8x + 12

8x - 5x = -15 -12

3x = -27

x = -9

Hope this will help U

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Answer 2

★ How to do :-

Here, we are given with an equation that has some constants and two variables that have the same value. We are asked to find the value of the same variable x. We can find the value of those variables by some other concepts useful here. The concept used here is the cross multiplication in which we multiply the numerator of first fraction with the denominator of second fraction and vise versa. While cross multiplying the numbers in fraction, we get two separate equations and then, we can find the value of x by shifting the constants and variables together. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{4}{x - 3} = \dfrac{5}{(2x + 3)}}$

Cross multiply the numbers.

${\tt \leadsto 4 \: (2x + 3) = 5 \: (x - 3)}$

Multiply the numbers outside of bracket with numbers in bracket.

${\tt \leadsto 8x + 12 = 5x - 15}$

Shift the constants on RHS and variables on LHS.

${\tt \leadsto 8x - 5x = (-15) - 12}$

Subtract the values on LHS and RHS.

${\tt \leadsto 3x = (-27)}$

Shift the number 3 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{(-27)}{3}}$

Simplify the fraction to get the value of x.

${\tt \leadsto x = (-9)}$

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${\red{\underline{\boxed{\bf So, \: the \: value \: of \: x \: is \: \: (-9)}}}}$

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Verification :-

${\tt \leadsto \dfrac{4}{x - 3} = \dfrac{5}{(2x + 3)}}$

Substitute the value of x.

${\tt \leadsto \dfrac{4}{(-9) - 3} = \dfrac{5}{2 \times (-9) + 3}}$

Subtract the values on LHS and multiply the values on RHS, in denominators.

${\tt \leadsto \dfrac{4}{(-12)} = \dfrac{5}{(-18) + 3)}}$

Add the value son RHS, in denominator.

${\tt \leadsto \dfrac{4}{(-12)} = \dfrac{5}{(-15)}}$

Write the fractions in lowest form by cancellation method.

${\tt \leadsto \dfrac{1}{(-3)} = \dfrac{1}{(-3)}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!