SOLUTION: 24a-8-10a=-2(4-7a)

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Question 18975: 24a-8-10a=-2(4-7a)
Answer by Alwayscheerful(414) About Me  (Show Source):
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Solved by pluggable solver: EXPLAIN simplification of an expression
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YOUR ANSWER


  • Graphical form: Equation 24a-8-10a=-2%2A%284-7a%29 was fully solved.
  • Text form: 24a-8-10a=-2*(4-7a) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+24a-8-10a=-2%2A%284-7a%29+%29
    For tutors: simplify_cartoon( 24a-8-10a=-2*(4-7a) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 24%2Aa-highlight_red%28+8+%29-10%2Aa=-2%2A%284-7a%29.
Moved -8 to the right of expression
It becomes 24%2Aa-10%2Aa-highlight_green%28+8+%29=-2%2A%284-7a%29.
Look at highlight_red%28+24%2Aa+%29-highlight_red%28+10%2Aa+%29-8=-2%2A%284-7a%29.
Eliminated similar terms highlight_red%28+24%2Aa+%29,highlight_red%28+-10%2Aa+%29 replacing them with highlight_green%28+%2824-10%29%2Aa+%29
It becomes highlight_green%28+%2824-10%29%2Aa+%29-8=-2%2A%284-7a%29.
Look at %28highlight_red%28+24+%29-highlight_red%28+10+%29%29%2Aa-8=-2%2A%284-7a%29.
Added fractions or integers together
It becomes %28highlight_green%28+14+%29%29%2Aa-8=-2%2A%284-7a%29.
Look at highlight_red%28+%28highlight_red%28+14+%29%29%2Aa+%29-8=-2%2A%284-7a%29.
Remove unneeded parentheses around factor highlight_red%28+14+%29
It becomes highlight_green%28+14+%29%2Aa-8=-2%2A%284-7a%29.
Look at 14%2Aa-8=-2%2A%28highlight_red%28+4+%29-7%2Aa%29.
Moved 4 to the right of expression
It becomes 14%2Aa-8=-2%2A%28-7%2Aa%2Bhighlight_green%28+4+%29%29.
Look at 14%2Aa-8=highlight_red%28+-2%2A%28-7%2Aa%2B4%29+%29.
Moved these terms to the left highlight_green%28+2%2A%28-7%2Aa%2B4%29+%29
It becomes 14%2Aa-8%2Bhighlight_green%28+2%2A%28-7%2Aa%2B4%29+%29=0.
Look at 14%2Aa-highlight_red%28+8+%29%2B2%2A%28-7%2Aa%2B4%29=0.
Moved -8 to the right of expression
It becomes 14%2Aa%2B2%2A%28-7%2Aa%2B4%29-highlight_green%28+8+%29=0.
Look at 14%2Aa%2Bhighlight_red%28+2%2A%28-7%2Aa%2B4%29+%29-8=0.
Expanded term 2 by using associative property on %28-7%2Aa%2B4%29
It becomes 14%2Aa-highlight_green%28+2%2A7%2Aa+%29%2Bhighlight_green%28+2%2A4+%29-8=0.
Look at 14%2Aa-highlight_red%28+2+%29%2Ahighlight_red%28+7+%29%2Aa%2B2%2A4-8=0.
Multiplied numerator integers
It becomes 14%2Aa-highlight_green%28+14+%29%2Aa%2B2%2A4-8=0.
Look at 14%2Aa-14%2Aa%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+4+%29-8=0.
Multiplied numerator integers
It becomes 14%2Aa-14%2Aa%2Bhighlight_green%28+8+%29-8=0.
Look at 14%2Aa-14%2Aa%2Bhighlight_red%28+8+%29-highlight_red%28+8+%29=0.
Added fractions or integers together
It becomes 14%2Aa-14%2Aa%2Bhighlight_green%28+0+%29=0.
Look at 14%2Aa-14%2Aa%2Bhighlight_red%28+0+%29=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes 14%2Aa-14%2Aa=0.
Look at highlight_red%28+14%2Aa+%29-highlight_red%28+14%2Aa+%29=0.
Eliminated similar terms highlight_red%28+14%2Aa+%29,highlight_red%28+-14%2Aa+%29 replacing them with highlight_green%28+%2814-14%29%2Aa+%29
It becomes highlight_green%28+%2814-14%29%2Aa+%29=0.
Look at highlight_red%28+%2814-14%29%2Aa+%29=0.
Since highlight_red%28+%2814-14%29%2Aa+%29 has zero as a factor, it should be replaced with a zero
Look at 0=0.
Added fractions or integers together
It becomes 0=0.
Result: 0=0

Universal Simplifier and Solver


Done!

Hope this helps!