How do you solve |5x-6|=3?

2 Answers
Dec 27, 2016

Answer:

#x = 9/5# and #x = 3/5#

Explanation:

Because this problem contains the absolute value function we need to give it special attention.

The absolute value function transforms a negative or a positive number into a positive number.

Therefore, we need to solve the term inside the absolute value for both the positive and negative value it is equated to, in this case +3 and -3.

Solution 1)

#5x - 6 = 3#

#5x - 6 + color(red)(6) = 3 + color(red)(6)#

#5x - 0 = 9#

#5x = 9#

#(5x)/color(blue)(5) = 9/color(blue)(5)#

#(color(blue)(cancel(color(black)(5)))x)/cancel(color(blue)(5)) = 9/color(blue)(5)#

#x = 9/5#

Solution 2)

#5x - 6 = color(red)(-3)#

#5x - 6 + color(red)(6) = -3 + color(red)(6)#

#5x - 0 = 3#

#5x = 3#

#(5x)/color(blue)(5) = 3/color(blue)(5)#

#(color(blue)(cancel(color(black)(5)))x)/cancel(color(blue)(5)) = 3/color(blue)(5)#

#x = 3/5#

Dec 27, 2016

Answer:

#x=3/5" and "x=9/5# are solutions

Explanation:

Given:#" "|5x-6|=3#

So in effect we have:

#|+-3|=+3#

So everything inside the | | must end up as positive or negative 3.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Set "5x-6=-3)#

Add 6 to both sides

#5x=+3#

Divide both sides by 5

#color(blue)(x=+3/5)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Set "5x-6=+3)#

Add 6 to both sides

#5x=+9#

Divide both sides by 5

#color(blue)(x=+9/5)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(green)("Putting it all together")#

#|5x-6|=+3#

#x=3/5" and "x=9/5# are solutions