How do you solve #|3z - 4| = | 5z - 6|#?

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Answer 1 · 2018-04-03T22:40:56

#z_1=1# and #z_2=5/4#

#|3z-4|=|5z-6|#

After squaring both sides for removing sign of absolute value

#(3z-4)^2=(5z-6)^2#

#9z^2-24z+16=25z^2-60z+36#

#16z^2-36z+20#

#4z^2-9z+5=0#

#(z-1)*(4z-5)=0#

Hence #z_1=1# and #z_2=5/4#