How do you solve #y=|10x-2|-7#?

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Answer 1 · 2018-03-20T12:20:33

Zeros: #x_1=9/10#, #x_2=-1/2#

Let #y=0# and solve for #x# to find zeros of this function.

#abs(10x-2)-7=0#
#abs(10x-2)=7#

#10x-2# lies within the absolute value operator, therefore either #10x-2=color(blue)(7)# or #10x-2=color(blue)(-7)# will satisfy the equation.

Case 1:
#10x-2=7#
#x=(7+2)/10=9/10#

Case 2:
#10x-2=-7#
#x=(-7+2)/10=-5/10=-1/2#

Therefore #x_1=-7#, #x_2=-1/2#

As seen from the graph:
graph{abs(10x-2)-7 [-2, 2, -5, 5]}