Question

How do you solve `6x + 4= 4( 3/ 2x + 1)`?

Answer 1

Correcting the equations as
`color(red)(6x + 4 = 4*((3/2)x + 1))`

`x = -1`

Explanation:

Remove the brackets first.
`6x + 4 = 4*(3/2)*x +4`
`6x + 4 = 6x + 4`

As the LHS & RHS are same, this cannot be solved.

By changing the coefficient of x in RHS, we will try to solve.

Correct the given equation as
`6x + 4 = 4(color(red)(3/4)x + 1)`

Removing brackets,
`6x + 4 =cancel( 4)*(3/cancel(4))*x +1`
`6x + 4 = 3x + 1`

Bringing x terms to LHS & constants to RHS,

`6x - 3x = 1 - 4`
`3x = -3`
`x = -1`

Answer 2

All real numbers are solutions.

Explanation:

`6x + 4 = 4(3/2 x +1)`
Use the distributive property.
`6x + 4 = (4)(3/2x)+(4)(1)`
`6x + 4 = 12/2 x + 4`
`6x + 4 = 6x + 4`
Subtract `6x` from both sides
`6x + 4 - 6x= 6x + 4-6x`
`4=4`
Subtract `4` from both sides
`4-4=4-4`
`0=0`

All real numbers are solutions.