Question

How do you solve `3abs(2x-6)= 4x-7`?

Answer 1

`x = 5/2 " or " x = 11/2`

Explanation:

Method 1:
`3|2x-6| = 4x-7`
Take the square on both sides to remove the modulus sign
`9(2x-6)^2 = (4x-7)^2`
`9(4x^2-24x+36) = 16x^2 - 56x + 49`
`4x^2-32x+55 = 0`
`(2x - 5)(2x - 11) = 0`
`x = 5/2 " or " x = 11/2`

Check that both solutions are correct since we squared the initial equation.

Method 2:
`3|2x-6| = 4x-7`
`3(2x-6) = 4x-7 " or " -3(2x-6) = 4x-7`
`2x = 11 " or " 10x = 25`
`x = 11/2 " or " x = 5/2`

graph{(3|2x-6|-y)(4x-7-y) = 0 [-5, 10, -40, 40]}