Question #a3e2c

2 Answers
Oct 28, 2017

Answer:

#x = 17/36#

Explanation:

We can set up an equation to solve the value of the number, #x#.

The number #= x#

Multiplying the number by #3 = 3x#

Subtracting #2/3# from that #= 3x - 2/3#

The result is #3/4#, so

#3x - 2/3 = 3/4#

We can then solve our equation:

#3x - 2/3 = 3/4#

Add #2/3# to both sides:

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

#3x = 17/12#

Divide both sides by #3# to get the value of #x#:

#x = 17/36#

You can then check your answer (optional):

#17/36 * 3 = 17/12#

#17/12 - 2/3 = 3/4#

Oct 28, 2017

Answer:

#17/36#

Explanation:

Breaking the question down into its component parts.

A number ......................................................... #x#
is multiplied by 3 ...........................................#3x#
and #2/3# is subtracted from the number ....#3x-2/3#
The result is #3/4#................................................#3x-2/3=3/4#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The wording of this question could be tidied up a bit. There are issues with it.

#color(blue)("Step 1 - isolate the term with "x" in it")#

Add #2/3# to both sides turning the left hand side #-2/3# into 0

#color(green)(3x-2/3color(red)(+2/3)color(white)("dd")=color(white)("dd")3/4color(red)(+2/3)#

#3x+0=3/4+2/3#

#3xcolor(white)("ddd")=3/4+2/3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 2 - simplify the right hand side")#

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

#color(green)(3x=[3/4color(red)(xx1)]+[2/3color(red)(xx1)]#

#color(green)(3x=[3/4color(red)(xx3/3)]+[2/3color(red)(xx4/4)]#

#3x=color(white)("dd")9/12color(white)("ddd")+color(white)("ddd")8/12color(white)("ddd") = 17/12#

#3x=17/12#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 3 - isolate "x)#

Multiply both sides by #1/3# - turns the 3 from #3x# into 1 and #1xx x= x#

#x=17/12xx1/3 = 17/36#

17 is a prime number so we can not simplify the fraction any further.