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How do you solve this equation? `14+2/(x-1)=10`

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rawrhappy | Student, Grade 10 | Honors

Posted August 15, 2013 at 12:50 AM via web

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How do you solve this equation?

`14+2/(x-1)=10`

2 Answers | Add Yours

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mjripalda | High School Teacher | (Level 3) Educator

Posted August 15, 2013 at 1:10 AM (Answer #1)

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`14+2/(x-1)=10`

Notice that the x is in the denominator. So, it must be removed in the denominator in order to have x only at one side of the equation.

To do so, multiply both sides by the denominator x-1.

`(x-1)*(14+2/(x-1))=10*(x-1)`

`14(x-1)+2=10(x-1)`

`14x-14+2=10x-10`

Then, combine like terms.

`14x-12=10x-10`

`14x-10x-12=10x-10x-10`

`4x-12=-10`

`4x-12+12=-10+12`

`4x=2`

And divide both sides by 4.

`(4x)/x=2/4`

`x=1/2`

Hence, the solution to the given equation is `x=1/2` .

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user8235304 | Student, Grade 11 | Valedictorian

Posted August 15, 2013 at 2:12 AM (Answer #2)

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`14 + 2/(x-1) = 10`

Now, `` `x-1 != 0` Therefore, `x!=1` .Ans.

Now, `2/(x-1) = 10 - 14 = -4`

hence;      `x-1 = (2/-4)`

 hence;     `x-1 = -(1/2)`

 hence;     `x=-(1/2) + 1`

 hence;     `x=(1/2)` Ans.

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