Question

Find the solutions to the rational equation:

x+2 2x-4
3
2
(2 pts)
A
X = 2
B
x = 6
с
x = -2
D
x = 4

Answer 1

D

Explanation:

`(x+2)/(3)` =
`(2x-4)/(2)` ( cross- multiply )

3(2x - 4) = 2(x + 2) ← distribute parenthesis on both sides

6x - 12 = 2x + 4 ( subtract 2x from both sides )

4x - 12 = 4 ( add 12 to both sides )

4x = 16 ( divide both sides by 4 )

x = 4

Answer 2

Question : -

`\longrightarrow (x + 2)/(3) = (2x - 4)/(2)`

What to Find : -

In this question we have to find the value of x .

Let's Get start Solving : -

`\longrightarrow (x + 2)/(3) = (2x - 4)/(2)`

So , by cross multiplying :

`\longrightarrow \: 2(x + 2) = 3(2x - 4)`

Now , calculation left hand side as well as right hand side :

`\longrightarrow \: 2x + 4 = 6x - 12`

Now , transposing 6x to left hand side and 4 to right hand side :

`\longrightarrow \: 2x - 6x = - 12 - 4`

Now , solving left hand side and right hand side :

`\longrightarrow \: - 4x = - 16`

As negative sign is present on both the side , so it will cancel out :

`\longrightarrow \: \cancel - 4x = \cancel- 16`

Now we have :

`\longrightarrow \: 4x = 16`

Now we are transposing 4 to right side and it will change into division from multiplication :

`\longrightarrow \: x = \cancel (16)/(4)`

So we get :

`\longrightarrow \: \green{ \boxed{ \bold x = 4}}`

• Therefore value of x is 4 .

Verification : -

We are verifying our answer by putting value of x in given question :

`\longrightarrow (4 + 2)/(3) = (2(4) - 4)/(2) \:`

Solving ,

`\longrightarrow \: (6)/(3) = (8 - 4)/(2)`

Now subtracting 8 and 4 :

`\longrightarrow \: (6)/(3) = (4)/(2)`

Now , dividing 6 by 3 and 4 by 2 :

`\longrightarrow \cancel{(6)/(3) } = \cancel{(4)/(2) }`

We get :

`\longrightarrow \: \bold{2 = 2}`

That means ,

`\longrightarrow L.H.S = R.H.S`

• Hence Verified .

Therefore our answer is correct .

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