Question

1/6(3x − 6) = 1/8(4x + 8)
what is x???

Answer 1

This equation doesn't have any real solutions.

Explanation:

1. Write the expression.

`(1)/(6) (3x-6)=(1)/(8) (4x+8)`

2. Multiply to solve the parentheses on both sides.

Here, we apply the distributive property of multiplication (check attached image 1).

`((1)/(6) )(3x)+((1)/(6))(-6)=((1)/(8))(4x)+((1)/(8))(8)\\ \\(3x)/(6) +((-6)/(6))=((4x)/(8) )+((8)/(8) )\\ \\(1)/(2) x+(-1)=(1)/(2)x+1\\ \\(1)/(2) x-1=(1)/(2)x+1`

3. Add "1" to both sides of the equation.

`(1)/(2) x-1+1=(1)/(2)x+1+1\\ \\(1)/(2) x=(1)/(2)x+2`

4. Subtract
`(1)/(2) x` from both sides of the equation.

`(1)/(2) x-(1)/(2) x=(1)/(2)x+2-(1)/(2) x\\ \\0=2`

5. Conclude.

This equation doesn't have any real solutions, because when we got a false statement (0=2) when attempting to solve it.

Check attached image 2 to see a representation of this problem.

See how the lines never meet, that means that there isn't an x value that makes these lines meet, because they have the same slope, making them be parallel to each other. Therefore, there's not a real solution for this problem.