Question

How many solutions exist for given equation?
1/2)x+12=4x-1

Answer 1

One solution.

Explanation:

1/2x + 12 = 4x - 1

12 + 1 = 4x - 1/2 x

13 = 7/2 x

x = 13 *2/7 = 26/7.

Answer 2

There is one solution for the equation.

Exact Form:

`x=(26)/(7)`

Decimal Form:

`x=3.714285...`

Mixed Number Form:

`x=3(5)/(7)`

Explanation:

Combine
`(1)/(2)` and x.

`(x)/(2) +12=4x-1`

Move all terms containing x to the left side of the equation.

Subtract 4x from both sides of the equation.

`(x)/(2) +12-4x=-1`

Simplify the left side of the equation.

To write
`(-4x)/(1)` as a fraction with a common denominator, multiply by
`(2)/(2)`.

`(x)/(2) +(-4x)/(1) *(2)/(2) +12=-1`

Write each expression with a common denominator of 2, by multiplying each by an appropriate factor of 1.

Combine

`(x)/(2)+(-4x*2)/(1*2) +12=-1`

Multiply 2 by 1.

`(x)/(2) +(-4x*2)/(2) +12=-1`

Combine the numerators over the denominator.

`(x-4x*2)/(2) +12=-1`

Simplify each term

Simplify the numerator

Factor x out of x - 4x * 2

Raise x to the power of 1.

`(x-4x*2)/(2) +12=-1`

Factor x out of
`x^(1)`

`(x*1-4x*2)/(2) +12=-1`

Factor x out of -4x * 2

`(x*1+x(-4*2))/(2) +12=-1`

Factor x out of x * 1 + x (-4 * 2).

`(x(1-4*2))/(2) +12=-1`

Multiply -4 by 2.

`(x(1-8))/(2) +12=-1`

Subtract 8 from 1.

`(x*-7)/(2) +12=-1`

Move -7 to the left of x.

`(-7*x)/(2) +12=-1`

Move the negative in front of the fraction.

`-(7x)/(2) +12=-1`

Move all terms not containing x to the right side of the equation.

Subtract 12 from both sides of the equation.

`-(7x)/(2) =-1-12`

Subtract 12 from -1.

`-(7x)/(2) =-13`

Multiply both sides of the equation by
`-(2)/(7)`.

`-(2)/(7) *(-(7x)/(2))=-(2)/(7) *-13`

Simplify both sides of the equation.

Simplify the left side

Cancel the common factor of 2.

Move the leading negative in
`-(2)/(7)` into the numerator.

`(-2)/(7) *-(7x)/(2) =-(2)/(7) *-13`

Move the leading negative in
`-(7x)/(2)` into the numerator.

`(-2)/(7) *(-7x)/(2) =-(2)/(7) *-13`

Factor out the greatest common factor 2.

`(2*-1)/(7) *(-7x)/(2*1) =-(2)/(7) *-13`

Cancel the common factor

`(-1)/(7) (-7x)/(1) =-(2)/(7) *-13`

Cancel the common factor of 7.

Factor out the greatest common factor 7.

`(-1)/(7(1)) *(7(-x))/(1) =-(2)/(7) *-13`

Cancel the common factor.

`(-1)/(1) *(-x)/(1) =-(2)/(7) *-13`

Simplify

Multiply
`(-1)/(1)` and
`(-x)/(1)`.

`(x)/(1) =-(2)/(7) *-13`

Multiply -1 by -1.

`(1x)/(1) =-(2)/(7) *-13`

Multiply x by 1.

`(x)/(1) =-(2)/(7) *-13`

Divide x by 1.

`x=-(2)/(7) *-13`

Multiply
`-(2)/(7) * -13`

Multiply -13 by -1.

`x=13((2)/(7) )`

Combine 13 and
`(2)/(7)`.

`x=(13*2)/(7)`

Multiply 13 by 2.

`x = (26)/(7)`

The result can be shown in multiple forms.

Exact Form:

`x=(26)/(7)`

Decimal Form:

`x=3.714285...`

Mixed Number Form:

`x=3(5)/(7)`