Question

Solve the equation.

-1/6x-5=2/3x

A. x= - 6.
B. x = -5.
C. x = 3.
D. x = 6.

Answer 1

A. x = -6

Explanation:

-1/6x - 5 = 2/3x

add 1/6x to both sides:

-1/6x - 5 + 1/6x = 2/3x + 1/6x

-5 = 2/3x + 1/6x

common denominator on right side:

-5 = 4/6x + 1/6x

combine right side:

-5 = 5/6x

multiply both sides by 6/5:

(-5)(6/5) = (5/6x)(6/5)

-30/5 = x

reduce left side:

-6 = x

x = -6 (option a)

Answer 2

Answer: A) x=-6

Step by step explanation:

`\boldsymbol{\sf{(-1)/(6)x-5=(2)/(3)x }}`

We calculate the multiplication expression.

`\boldsymbol{\sf{(-1)/(6)x-5=(2)/(3)x \iff \ -(x)/(6)-5=(2)/(3) x \iff -(x)/(6)-5=(2x)/(3) }}`

Eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

`\boldsymbol{\sf{ -(x)/(6)-5=(2x)/(3) \iff \ -x-30=4x}}`

The variable is moved to the left and the symbol is changed.

`\boldsymbol{\sf{-x-30=4x \iff -x-30-4x=0}}`

We move the constant to the right side and change the sign.

`\boldsymbol{\sf{-x-30-4x=0 \iff -x-4x=30}}`

`\boldsymbol{\sf{-x-4x=30 \ < == We \ organize \ the \ equation== > \ -5x=30 }}`

`\bf{\underline{Change \ the \ sign \ on \ both \ sides \ of \ the \ equation.}}`

`\boldsymbol{\sf{-5x=30 \iff \ 5x=-30 \ < ==Split== > \ x=-(30)/(5)=\boxed{\boxed{\boldsymbol{\sf{-6}}}} }}`