How do you solve #| 1/2-3/4x | + 1=3 #?

2 Answers
Mar 2, 2016

Answer:

#-#2 and 10/3.

Explanation:

The given equation is equivalent to the pair 1/2#-#3 x/4 = #+-#2.

Mar 2, 2016

Answer:

#x = -2" or "x=10/3" "#Note that #10/3 = 3.33bar3#

Explanation:

The very nature of this type of problem is that it usually has 2 solutions for #x#

We need to end up with the 'Absolute' part of the equation on its own and on the left of the equals sign and everything else on the other.

Given:#" "color(brown)(|1/2-3/4 x|+1=3)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Simplifying")#

Subtract #color(blue)(1)# from both sides

#" "color(brown)(|1/2-3/4 x|+1color(blue)(-1)" "=" "3color(blue)(-1))#

#" "|1/2-3/4 x|+0" "=" "2#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Solving for "x)#

Think of this as:

#" "|1/2-3/4 x|" "=" "|+-2|#

#color(brown)("Consider: "1/2-3/4 x" "=" "-2" "#

Multiply by (-1 ) giving

#" "-1/2+3/4 x=+2#

#" "3/4 x=2+1/2#

#color(blue)(" " x" "=" "4/3xx5/2" " = " "10/3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(brown)("Consider: "1/2-3/4 x=+2#

Multiply by (-1 ) giving

#" "-1/2+3/4 x=-2#

#" "3/4 x=-2+1/2#

#" "color(blue)(x=4/3xx(-3/2) = -2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#" "color(magenta)(x = -2" or "x=10/3)#

Tony B