Question

the remainders are in proportion!
If (x - 2), (x + 2), (2x + 1) and (2x + 19) are in proportion, find the
value of x
​

Answer 1

Answer:

The answer is 4.

Step-by-step explanation:

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Answer 2

Answer:

$\rm \: x = 4$

Explanation:

Given that,

$\rm \: (x - 2)(x + 2)(2x + 1)(2x + 19) \: are \: in \: proportion \:$

We need to find the value of x

Doing a proportional analysis : -

$\rm \: (x - 2) : (x + 2) : : (2x + 1) : (2x + 19)$

On solving further,

$\rm \implies \: \dfrac{(x - 2)}{(x + 2)} = \dfrac{(2x + 1)}{(2x + 19)}$

$\rm \implies \:(x - 2)(2x + 19) = (2x + 1)(x + 2)$

$\rm \implies \:2 {x}^{2} - 4x + 19x - 38 = {2x}^{2} + x + 4x + 2$

$\rm \implies \:2 {x}^{2} + 15x - 38 = {2x}^{2} + 5x + 2$

$\rm \implies \: 15x - 38 =5x + 2$

$\rm \implies \: 15x - 5x =38 + 2$

$\rm \implies \: 10x =40$

$\rm \implies \: x = \dfrac{40}{10}$

$\rm \implies \: x =4$

∴ The value of x is 4

_____________________

Verification:

$\rm \implies \: \dfrac{(x - 2)}{(x + 2)} = \dfrac{(2x + 1)}{(2x + 19)}$

$\rm \: substitute \: x = 4$

$\rm \implies \: \dfrac{4 - 2}{4 + 2} = \dfrac{2(4) + 1}{2(4) + 19}$

$\rm \implies \: \dfrac{2}{6} = \dfrac{8 + 1}{8 + 19}$

$\rm \implies \: \dfrac{1}{3} = \dfrac{9}{27}$

$\rm \implies \: \dfrac{1}{3} = \dfrac{1}{3}$

∵ L. H. S. = R. H. S.

Hence, verified !!