Question

Which methods correctly solve for variable x in the equation 3/4 (x - 8)=6?

Answer 1

The equation given is

`(3)/(4)(x-8)=6`

Step1

Multiply both sides by

`(4)/(3)`

We have

`\begin{gathered} (4)/(3)*(3)/(4)(x-8)=(4)/(3)*6 \\ \\ x-8=8 \end{gathered}`

Step2

Add 8 to both sides of the equation

`\begin{gathered} x-8+8=8+8_{} \\ x=16 \end{gathered}`

Therefore, the correct method that solves the equation is

5. Multiply both sides by 4/3 and then add 8 to both sides of the equation

similarly,

Distribute 3/4 to (x-8)

`\begin{gathered} (3)/(4)(x-8)=6 \\ (3)/(4)x-6=6 \end{gathered}`

Then add 6 to both sides

`\begin{gathered} (3)/(4)x-6=6 \\ \\ (3)/(4)x-6+6=6+6 \\ (3)/(4)x=12 \end{gathered}`

Then multiply both sides by 4/3

`\begin{gathered} (3)/(4)x*(4)/(3)=12*(4)/(3) \\ \\ x=16 \end{gathered}`

Hence

2. Distribute 3/4 to (x-8), then add 6 to both sides and finally multiply both sides by 4/3

Therefore

Distribute 3/4 to (x-8), then add 6 to both sides and finally multiply both sides by 4/3

and