Question

solve the equations:. 6 divided by 2x-(3-4x) =2/3​

Answer 1

Step-by-step explanation:

6/2x-(3-4x)=2/3

6/2x-3+4x=2/3

6/6x-3=2/3

12x-6=18

12x=18+6

12x=24

X=24/12

X =2

Answer 2

Question

Solve the equation -: $\dfrac{6}{2x-(3-4x)}= \dfrac{2}{3}$

_______________________________

Answer

Let's solve your equation step-by-step.

$\dfrac{6}{2x-(3-4x)}= \dfrac{2}{3}$

Step 1: Simplify the equation.

$\implies \dfrac{6}{2x-(3-4x)}= \dfrac{2}{3}$

[We changed sign of -4x to +4x because - × - = +]

$\implies \dfrac{6}{2x-3+4x}= \dfrac{2}{3}$

[Combine Like Terms]

$\implies \dfrac{6}{2x+4x-3}= \dfrac{2}{3}$        

$\implies \dfrac{6}{6x-3}= \dfrac{2}{3}$

Step 2: Cross Multiply.

$\implies \dfrac{6}{6x-3}= \dfrac{2}{3}$

$\implies 2(6x-3) = 3(6)$

$\implies 12x-6 = 18$

Step 3: Add 6 to both sides of the equation.

$\implies 12x-6+6 = 18+6$

$\implies 12x= 24$

Step 4: Divide 1 from both sides of the equation.

$\implies \dfrac{12x}{12}= \dfrac{24}{12}$

$\implies x = 2$

_______________________________

Let's do the verification for the value of 'x' step-by-step.

$\dfrac{6}{2x-(3-4x)}= \dfrac{2}{3}$

Step 1: Substitute the value of 'x' and simplify.

$\implies \dfrac{6}{2(2)-(3-4(2))}= \dfrac{2}{3}$

$\implies \dfrac{6}{4-(3-8)}= \dfrac{2}{3}$

$\implies \dfrac{6}{4-(-5)}= \dfrac{2}{3}$

$\implies \dfrac{6}{4+5}= \dfrac{2}{3}$

$\implies \dfrac{6}{9}= \dfrac{2}{3}$

$\implies \dfrac{2}{3}= \dfrac{2}{3}$

∴ LHS = RHS

∴ x = 2 in the given equation.

_______________________________