Question

solve 2x- 8 / 5x + 2 = 3/2​

Answer 1

Question :-

Solve -

$\rm \dfrac{2x - 8}{5x + 2} = \dfrac{3}{2}$

Solution :-

$\rm \dfrac{2x - 8}{5x + 2} = \dfrac{3}{2}$

By cross multiplication :-

➩ $\rm 2(2x - 8) = 3(5x + 2)$

➩ $\rm 4x - 16 = 15x + 6$

➩ $\rm 15x - 4x = - 16 - 6$

➩ $\rm 11x = - 22$

➩ $\rm x = \dfrac{ - \cancel{ 22}}{\cancel {11}}$

➩ $\boxed{\rm x = - 2}$

Verification :-

➩ $\rm LHS = \dfrac{2x - 8}{5x + 2}$

➩ $\rm \dfrac{2( - 2) - 8}{5( - 2) + 2}$

➩ $\rm \dfrac{ - 4 - 8}{ - 10 + 2}$

➩ $\rm \dfrac{ - 12}{ - 8}$

➩ $\rm LHS = \frac{3}{2} = RHS$

Hence verified.

Answer 2

Step-by-step explanation:

Solve -

\rm \dfrac{2x - 8}{5x + 2} = \dfrac{3}{2}

5x+2

2x−8

=

2

3

Solution :-

\rm \dfrac{2x - 8}{5x + 2} = \dfrac{3}{2}

5x+2

2x−8

=

2

3

By cross multiplication :-

➩ \rm 2(2x - 8) = 3(5x + 2)2(2x−8)=3(5x+2)

➩ \rm 4x - 16 = 15x + 64x−16=15x+6

➩ \rm 15x - 4x = - 16 - 615x−4x=−16−6

➩ \rm 11x = - 2211x=−22

➩ \rm x = \dfrac{ - \cancel{ 22}}{\cancel {11}}x=

11

−

22

➩ \boxed{\rm x = - 2}

x=−2

Verification :-

➩ \rm LHS = \dfrac{2x - 8}{5x + 2}LHS=

5x+2

2x−8

➩ \rm \dfrac{2( - 2) - 8}{5( - 2) + 2}

5(−2)+2

2(−2)−8

➩ \rm \dfrac{ - 4 - 8}{ - 10 + 2}

−10+2

−4−8

➩ \rm \dfrac{ - 12}{ - 8}

−8

−12

➩ \rm LHS = \frac{3}{2} = RHSLHS=

2

3

=RHS

Hence verified.