Question

Determine whether the equation is always, sometimes, or never true.

2/3 x + 4 = 2x

Answer 1

Always true

Explanation:

Given

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

Required

Determine its type of solution

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

Collect Like Terms

`2x - (2)/(3)x = 4`

Take LCM

`(6x - 2x)/(3) = 4`

`(4x)/(3) = 4`

Multiply both sides by
`(3)/(4)`

`(4x)/(3) * (3)/(4)= 4 * (3)/(4)`

`x = 4 * (3)/(4)`

`x = 3`

Hence, the equation is always true for x = 3