Question

solve $\frac { ( 4 x + 4 ) - ( 7 x - 8 ) } { 4 x + 5 } = - \frac { 4 } { 3 }$

"find x"

​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given Equation:

$\rm:\longmapsto \dfrac{(4x + 4) - (7x - 8)}{4x + 5} =\dfrac{ - 4}{3}$

$\rm:\longmapsto \dfrac{4x + 4 - 7x +8}{4x + 5} =\dfrac{ - 4}{3}$

$\rm:\longmapsto \dfrac{ - 3x + 12}{4x + 5} =\dfrac{ - 4}{3}$

On cross multiplying, we get:

$\rm:\longmapsto 3( - 3x + 12) = - 4(4x + 5)$

$\rm:\longmapsto - 9x + 36 = -16x - 20$

$\rm:\longmapsto - 9x + 16x+ 36 = - 20$

$\rm:\longmapsto 7x+ 36 = - 20$

$\rm:\longmapsto 7x= - 20 - 36$

$\rm:\longmapsto 7x= -56$

$\rm:\longmapsto x= \dfrac{ - 56}{7}$

$\rm:\longmapsto x= - 8$

★ Therefore, the value of x satisfying the given equation is -8. (Answer)

$\textsf{\large{\underline{Verification}:}}$

Put x = 8 in equation, we get:

$\rm = \dfrac{(4x + 4) - (7x - 8)}{4x + 5}$

$\rm = \dfrac{( - 32 + 4) - ( -56 - 8)}{ - 32 + 5}$

$\rm = \dfrac{ - 28 + 64}{ - 27}$

$\rm = \dfrac{36}{ - 27}$

$\rm = \dfrac{4 \times 9}{ - 3 \times 9}$

$\rm = \dfrac{ - 4}{3}$

Therefore, our answer is correct (Verified).

Answer 2

Answer:

x = -8

Step-by-step explanation:

$\dfrac{(4x + 4) - (7x - 8)}{4x + 5} = \dfrac{ - 4}{3} \\ \\ \dfrac{4x + 4 - 7x + 8}{4x + 5} = \dfrac{ - 4}{3} \\ \\ \dfrac{ - 3x + 12}{4x + 5} = \dfrac{ - 4}{3} \\ \\ \sf{cross \: multiplying} \\ \\ - 9x + 36 = - 16x - 20 \\ \\ 7x = - 56 \\ \\ x = - 8$

Hence the value of x is -8.