SOLUTION: -4(a+1)-3a=7(2a-3)+3

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Question 213745: -4(a+1)-3a=7(2a-3)+3
Found 2 solutions by drj, jim_thompson5910:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
-4%28a%2B1%29-3a=7%282a-3%29%2B3

The following steps will solve the above problem

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: a=0.666666666666667.
  • Graphical form: Equation -4%2A%28a%2B1%29-3a=7%2A%282a-3%29%2B3 was fully solved.
  • Text form: -4*(a+1)-3a=7*(2a-3)+3 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-4%2A%28a%2B1%29-3a=7%2A%282a-3%29%2B3+%29
    For tutors: simplify_cartoon( -4*(a+1)-3a=7*(2a-3)+3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -4%2A%28a%2B1%29-3%2Aa=highlight_red%28+7%2A%282%2Aa-3%29%2B3+%29.
Moved these terms to the left highlight_green%28+-7%2A%282%2Aa-3%29+%29,highlight_green%28+-3+%29
It becomes -4%2A%28a%2B1%29-3%2Aa-highlight_green%28+7%2A%282%2Aa-3%29+%29-highlight_green%28+3+%29=0.
Look at -highlight_red%28+4%2A%28a%2B1%29+%29-3%2Aa-7%2A%282%2Aa-3%29-3=0.
Expanded term -4 by using associative property on %28a%2B1%29
It becomes -highlight_green%28+4%2Aa+%29-highlight_green%28+4%2A1+%29-3%2Aa-7%2A%282%2Aa-3%29-3=0.
Look at -4%2Aa-highlight_red%28+4+%29%2Ahighlight_red%28+1+%29-3%2Aa-7%2A%282%2Aa-3%29-3=0.
Multiplied numerator integers
It becomes -4%2Aa-highlight_green%28+4+%29-3%2Aa-7%2A%282%2Aa-3%29-3=0.
Look at -4%2Aa-highlight_red%28+4+%29-3%2Aa-7%2A%282%2Aa-3%29-highlight_red%28+3+%29=0.
Added fractions or integers together
It becomes -4%2Aa%2Bhighlight_green%28+-7+%29-3%2Aa-7%2A%282%2Aa-3%29=0.
Look at -4%2Aa%2Bhighlight_red%28+-7+%29-3%2Aa-7%2A%282%2Aa-3%29=0.
Moved -7 to the right of expression
It becomes -4%2Aa-3%2Aa-7%2A%282%2Aa-3%29%2Bhighlight_green%28+-7+%29=0.
Look at -4%2Aa-3%2Aa-7%2A%282%2Aa-3%29%2Bhighlight_red%28+-7+%29=0.
Removed extra sign in front of -7
It becomes -4%2Aa-3%2Aa-7%2A%282%2Aa-3%29-highlight_green%28+7+%29=0.
Look at -highlight_red%28+4%2Aa+%29-highlight_red%28+3%2Aa+%29-7%2A%282%2Aa-3%29-7=0.
Eliminated similar terms highlight_red%28+-4%2Aa+%29,highlight_red%28+-3%2Aa+%29 replacing them with highlight_green%28+%28-4-3%29%2Aa+%29
It becomes highlight_green%28+%28-4-3%29%2Aa+%29-7%2A%282%2Aa-3%29-7=0.
Look at %28-highlight_red%28+4+%29-highlight_red%28+3+%29%29%2Aa-7%2A%282%2Aa-3%29-7=0.
Added fractions or integers together
It becomes %28highlight_green%28+-7+%29%29%2Aa-7%2A%282%2Aa-3%29-7=0.
Look at %28highlight_red%28+-7+%29%29%2Aa-7%2A%282%2Aa-3%29-7=0.
Removed extra sign in front of -7
It becomes %28-highlight_green%28+7+%29%29%2Aa-7%2A%282%2Aa-3%29-7=0.
Look at highlight_red%28+%28-highlight_red%28+7+%29%29%2Aa+%29-7%2A%282%2Aa-3%29-7=0.
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes -highlight_green%28+7+%29%2Aa-7%2A%282%2Aa-3%29-7=0.
Look at -7%2Aa-highlight_red%28+7%2A%282%2Aa-3%29+%29-7=0.
Expanded term -7 by using associative property on %282%2Aa-3%29
It becomes -7%2Aa-highlight_green%28+7%2A2%2Aa+%29%2Bhighlight_green%28+7%2A3+%29-7=0.
Look at -7%2Aa-highlight_red%28+7+%29%2Ahighlight_red%28+2+%29%2Aa%2B7%2A3-7=0.
Multiplied numerator integers
It becomes -7%2Aa-highlight_green%28+14+%29%2Aa%2B7%2A3-7=0.
Look at -7%2Aa-14%2Aa%2Bhighlight_red%28+7+%29%2Ahighlight_red%28+3+%29-7=0.
Multiplied numerator integers
It becomes -7%2Aa-14%2Aa%2Bhighlight_green%28+21+%29-7=0.
Look at -7%2Aa-14%2Aa%2Bhighlight_red%28+21+%29-highlight_red%28+7+%29=0.
Added fractions or integers together
It becomes -7%2Aa-14%2Aa%2Bhighlight_green%28+14+%29=0.
Look at -highlight_red%28+7%2Aa+%29-highlight_red%28+14%2Aa+%29%2B14=0.
Eliminated similar terms highlight_red%28+-7%2Aa+%29,highlight_red%28+-14%2Aa+%29 replacing them with highlight_green%28+%28-7-14%29%2Aa+%29
It becomes highlight_green%28+%28-7-14%29%2Aa+%29%2B14=0.
Look at %28-highlight_red%28+7+%29-highlight_red%28+14+%29%29%2Aa%2B14=0.
Added fractions or integers together
It becomes %28highlight_green%28+-21+%29%29%2Aa%2B14=0.
Look at %28highlight_red%28+-21+%29%29%2Aa%2B14=0.
Removed extra sign in front of -21
It becomes %28-highlight_green%28+21+%29%29%2Aa%2B14=0.
Look at highlight_red%28+%28-highlight_red%28+21+%29%29%2Aa+%29%2B14=0.
Remove unneeded parentheses around factor highlight_red%28+21+%29
It becomes -highlight_green%28+21+%29%2Aa%2B14=0.
Look at highlight_red%28+-21%2Aa%2B14+%29=0.
Solved linear equation highlight_red%28+-21%2Aa%2B14=0+%29 equivalent to -21*a+14 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=0.666666666666667.

Universal Simplifier and Solver


Done!



ANSWER is 2%2F3 or 0.666667

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-4%28a%2B1%29-3a=7%282a-3%29%2B3 Start with the given equation.


-4a-4-3a=14a-21%2B3 Distribute.


-7a-4=14a-21%2B3 Combine like terms on the left side.


-7a-4=14a-18 Combine like terms on the right side.


-7a=14a-18%2B4 Add 4 to both sides.


-7a-14a=-18%2B4 Subtract 14a from both sides.


-21a=-18%2B4 Combine like terms on the left side.


-21a=-14 Combine like terms on the right side.


a=%28-14%29%2F%28-21%29 Divide both sides by -21 to isolate a.


a=2%2F3 Reduce.


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Answer:

So the solution is a=2%2F3 which approximates to a=0.667.