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

1 Answer
dani83
Aug 14, 2015

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]}

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