SOLUTION: solve each equation. 5-(3a-4)/5= (7-2a)/2

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Question 932166: solve each equation.
5-(3a-4)/5= (7-2a)/2
Found 2 solutions by srinivas.g, MathTherapy:
Answer by srinivas.g(540) 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: a=-5.75.
  • Graphical form: Equation 5-%283a-4%29%2F5=%287-2a%29%2F2 was fully solved.
  • Text form: 5-(3a-4)/5=(7-2a)/2 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5-%283a-4%29%2F5=%287-2a%29%2F2+%29
    For tutors: simplify_cartoon( 5-(3a-4)/5=(7-2a)/2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+5+%29-%283%2Aa-4%29%2F5=%287-2a%29%2F2.
Moved 5 to the right of expression
It becomes -%283%2Aa-4%29%2F5%2Bhighlight_green%28+5+%29=%287-2a%29%2F2.
Look at -%283%2Aa-4%29%2F5%2B5=%28highlight_red%28+7+%29-2%2Aa%29%2F2.
Moved 7 to the right of expression
It becomes -%283%2Aa-4%29%2F5%2B5=%28-2%2Aa%2Bhighlight_green%28+7+%29%29%2F2.
Look at -%283%2Aa-4%29%2F5%2B5=highlight_red%28+%28-2%2Aa%2B7%29%2F2+%29.
Moved these terms to the left highlight_green%28+-%28-2%2Aa%2B7%29%2F2+%29
It becomes -%283%2Aa-4%29%2F5%2B5-highlight_green%28+%28-2%2Aa%2B7%29%2F2+%29=0.
Look at -%283%2Aa-4%29%2F5%2Bhighlight_red%28+5+%29-%28-2%2Aa%2B7%29%2F2=0.
Moved 5 to the right of expression
It becomes -%283%2Aa-4%29%2F5-%28-2%2Aa%2B7%29%2F2%2Bhighlight_green%28+5+%29=0.
Look at -highlight_red%28+%283%2Aa-4%29%2F5+%29-%28-2%2Aa%2B7%29%2F2%2B5=0.
Expanded term -1%2F5 by using associative property on %283%2Aa-4%29
It becomes .
Look at .
Multiplied numerator integers
It becomes -highlight_green%28+3+%29%2F5%2Aa%2B1%2F5%2A4-%28-2%2Aa%2B7%29%2F2%2B5=0.
Look at -3%2F5%2Aa%2Bhighlight_red%28+1+%29%2F5%2Ahighlight_red%28+4+%29-%28-2%2Aa%2B7%29%2F2%2B5=0.
Multiplied numerator integers
It becomes -3%2F5%2Aa%2Bhighlight_green%28+4+%29%2F5-%28-2%2Aa%2B7%29%2F2%2B5=0.
Look at -3%2F5%2Aa%2Bhighlight_red%28+4%2F5+%29-%28-2%2Aa%2B7%29%2F2%2Bhighlight_red%28+5+%29=0.
Added fractions or integers together
It becomes -3%2F5%2Aa%2Bhighlight_green%28+29%2F5+%29-%28-2%2Aa%2B7%29%2F2=0.
Look at -3%2F5%2Aa%2Bhighlight_red%28+29%2F5+%29-%28-2%2Aa%2B7%29%2F2=0.
Moved 29%2F5 to the right of expression
It becomes -3%2F5%2Aa-%28-2%2Aa%2B7%29%2F2%2Bhighlight_green%28+29%2F5+%29=0.
Look at -3%2F5%2Aa-highlight_red%28+%28-2%2Aa%2B7%29%2F2+%29%2B29%2F5=0.
Expanded term -1%2F2 by using associative property on %28-2%2Aa%2B7%29
It becomes .
Look at -3%2F5%2Aa%2B1%2Fhighlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2Aa-1%2F2%2A7%2B29%2F5=0.
Factors 2 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes .
Look at -3%2F5%2Aa%2Bhighlight_red%28+1+%29%2F1%2Ahighlight_red%28+1+%29%2Aa-1%2F2%2A7%2B29%2F5=0.
Multiplied numerator integers
It becomes -3%2F5%2Aa%2Bhighlight_green%28+1+%29%2F1%2Aa-1%2F2%2A7%2B29%2F5=0.
Look at -3%2F5%2Aa%2B1%2F1%2Aa-highlight_red%28+1+%29%2F2%2Ahighlight_red%28+7+%29%2B29%2F5=0.
Multiplied numerator integers
It becomes -3%2F5%2Aa%2B1%2F1%2Aa-highlight_green%28+7+%29%2F2%2B29%2F5=0.
Look at -3%2F5%2Aa%2B1%2F1%2Aa-highlight_red%28+7%2F2+%29%2Bhighlight_red%28+29%2F5+%29=0.
Added fractions or integers together
It becomes -3%2F5%2Aa%2B1%2F1%2Aa%2Bhighlight_green%28+23%2F10+%29=0.
Look at -3%2F5%2Aa%2Bhighlight_red%28+1+%29%2Fhighlight_red%28+1+%29%2Aa%2B23%2F10=0.
Reduce similar several occurrences of highlight_red%28+1+%29 to
It becomes -3%2F5%2Aa%2Ba%2B23%2F10=0.
Look at -highlight_red%28+3%2F5%2Aa+%29%2Bhighlight_red%28+a+%29%2B23%2F10=0.
Eliminated similar terms highlight_red%28+-3%2F5%2Aa+%29,highlight_red%28+a+%29 replacing them with highlight_green%28+%28-3%2A1%2F5%2B1%29%2Aa+%29
It becomes highlight_green%28+%28-3%2A1%2F5%2B1%29%2Aa+%29%2B23%2F10=0.
Look at %28-highlight_red%28+3+%29%2Ahighlight_red%28+1+%29%2F5%2B1%29%2Aa%2B23%2F10=0.
Multiplied numerator integers
It becomes %28-highlight_green%28+3+%29%2F5%2B1%29%2Aa%2B23%2F10=0.
Look at %28-highlight_red%28+3%2F5+%29%2Bhighlight_red%28+1+%29%29%2Aa%2B23%2F10=0.
Added fractions or integers together
It becomes %28highlight_green%28+2%2F5+%29%29%2Aa%2B23%2F10=0.
Look at highlight_red%28+%28highlight_red%28+2%2F5+%29%29%2Aa+%29%2B23%2F10=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29,highlight_red%28+1%2F5+%29
It becomes highlight_green%28+2+%29%2Fhighlight_green%28+5+%29%2Aa%2B23%2F10=0.
Look at highlight_red%28+2%2F5%2Aa%2B23%2F10+%29=0.
Solved linear equation highlight_red%28+2%2F5%2Aa%2B23%2F10=0+%29 equivalent to 0.4*a+2.3 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=-5.75.

Universal Simplifier and Solver


Done!

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

solve each equation.
5-(3a-4)/5= (7-2a)/2


5+-+%283a+-+4%29%2F5+=+%287+-+2a%29%2F2

50 - 2(3a - 4) = 5(7 - 2a)}}} ------- Multiplying by LCD, 10

50 - 6a + 8 = 35 - 10a

58 - 6a = 35 - 10a

- 6a + 10a = 35 - 58

4a = - 23

a+=+%28-+23%29%2F4, or highlight_green%28system%28-+5%263%2F4_or%2C-+5.75%29%29