SOLUTION: Please explain how to solve 8(4-u)+u=8+u.

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Question 25321: Please explain how to solve 8(4-u)+u=8+u.
Found 2 solutions by Alwayscheerful, longjonsilver:
Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: u=3.
  • Graphical form: Equation 8%2A%284-u%29%2Bu=8%2Bu was fully solved.
  • Text form: 8*(4-u)+u=8+u simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+8%2A%284-u%29%2Bu=8%2Bu+%29
    For tutors: simplify_cartoon( 8*(4-u)+u=8+u )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 8%2A%28highlight_red%28+4+%29-u%29%2Bu=8%2Bu.
Moved 4 to the right of expression
It becomes 8%2A%28-u%2Bhighlight_green%28+4+%29%29%2Bu=8%2Bu.
Look at 8%2A%28-u%2B4%29%2Bu=highlight_red%28+8+%29%2Bu.
Moved 8 to the right of expression
It becomes 8%2A%28-u%2B4%29%2Bu=u%2Bhighlight_green%28+8+%29.
Look at 8%2A%28-u%2B4%29%2Bu=highlight_red%28+u%2B8+%29.
Moved these terms to the left highlight_green%28+-u+%29,highlight_green%28+-8+%29
It becomes 8%2A%28-u%2B4%29%2Bu-highlight_green%28+u+%29-highlight_green%28+8+%29=0.
Look at 8%2A%28-u%2B4%29%2Bhighlight_red%28+u+%29-highlight_red%28+u+%29-8=0.
Eliminated similar terms highlight_red%28+u+%29,highlight_red%28+-u+%29 replacing them with highlight_green%28+%281-1%29%2Au+%29
It becomes 8%2A%28-u%2B4%29%2Bhighlight_green%28+%281-1%29%2Au+%29-8=0.
Look at 8%2A%28-u%2B4%29%2Bhighlight_red%28+%281-1%29%2Au+%29-8=0.
Since highlight_red%28+%281-1%29%2Au+%29 has zero as a factor, it should be replaced with a zero
Look at 8%2A%28-u%2B4%29%2B0-8=0.
Added fractions or integers together
It becomes 8%2A%28-u%2B4%29%2B0-8=0.
Look at 8%2A%28-u%2B4%29%2Bhighlight_red%28+0+%29-8=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes 8%2A%28-u%2B4%29-8=0.
Look at highlight_red%28+8%2A%28-u%2B4%29+%29-8=0.
Expanded term 8 by using associative property on %28-u%2B4%29
It becomes -highlight_green%28+8%2Au+%29%2Bhighlight_green%28+8%2A4+%29-8=0.
Look at -8%2Au%2Bhighlight_red%28+8+%29%2Ahighlight_red%28+4+%29-8=0.
Multiplied numerator integers
It becomes -8%2Au%2Bhighlight_green%28+32+%29-8=0.
Look at -8%2Au%2Bhighlight_red%28+32+%29-highlight_red%28+8+%29=0.
Added fractions or integers together
It becomes -8%2Au%2Bhighlight_green%28+24+%29=0.
Look at highlight_red%28+-8%2Au%2B24+%29=0.
Solved linear equation highlight_red%28+-8%2Au%2B24=0+%29 equivalent to -8*u+24 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: u=3.

Universal Simplifier and Solver


Done!

Hope this helps!

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
First, get rid of the brackets so that we just have a collection of terms to add or subtract...

8(4-u)+u=8+u
32-8u+u = 8+u

Now collect like terms (i shall do it in 2 stages)
32-7u = 8+u
and then
32-8u = 8
-8u = -24

Now divide by -8 to find what u is:
u = -24/-8
u = +3

jon.