How do you solve #-7w + 2 = -3 #?

2 Answers
Jan 5, 2016

Answer:

Just put 'w' on one side and numbers on the other.

Explanation:

So from the starting equation it goes like this:

-7w +2 = -3 /-2
-7w = -5 /:(-7)
w = #(5)/"7"#

Jan 5, 2016

Answer:

#w=5/7#

#color(blue)("The tricks that show that the shortcuts actually work ")#

Explanation:

#color(blue)("Some thoughts!")#
#color(brown)("The other solution shows the shortcut methods which are both")# #color(brown)("very valid and speed everything up very much. This text explains")##color(brown)("the foundations upon which those shortcuts are based.")#

The objective is to have a single w on one side of the = and everything else on the other side. This format (equation) declares the worth of a single 'w'.

The w is already on the left hand side (LHS) so we do not need to move it.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 1")#
There is a 2 on the left so we need to 'get rid of it'

Subtract #color(blue)(2)# from both sides giving:

#color(brown)((-7w+2)color(blue)(-2)=(-3 )color(blue)(-2))#

#-7w +2-2=-3-2#

But #color(white)(..) +2-2=0" and "-3-2=-5color(white)(..)# giving:

#-7w+0=-5#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 2")#

Make #-7w" into "+7w#

Multiply both sides by #-1 # giving:

#7w=5#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Step 3")#

Isolate w
Divide both sides by 7 #(-: 7 " is the same as "color(blue)( xx1/7))#

#color(brown)(7wcolor(blue)(xx1/7)=5color(blue)(xx1/7))#

#7/7 w= 5/7#

But #7/7 =1# giving:

#w=5/7#