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

1 Answer
Aug 14, 2015

Answer:

# 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]}