SOLUTION: 4/3 + 2/3q = -5/3 - 1/3q - 4

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Question 556075: 4/3 + 2/3q = -5/3 - 1/3q - 4
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
We can multiply everything by 3 to clear out the fraction
4+2q=-5-1q-12
combine -5 and -12
4+2q=-17-q
add q to both sides
4+3q=-17
subtract 4 from both sides
3q=-21
divide by 3
q=-7
or to see it another way:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: q=-7.
  • Graphical form: Equation 4%2F3%2B%282%2F3%29%2Aq=-5%2F3-%281%2F3%29%2Aq-4 was fully solved.
  • Text form: 4/3+(2/3)*q=-5/3-(1/3)*q-4 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4%2F3%2B%282%2F3%29%2Aq=-5%2F3-%281%2F3%29%2Aq-4+%29
    For tutors: simplify_cartoon( 4/3+(2/3)*q=-5/3-(1/3)*q-4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2F3%2Bhighlight_red%28+%28highlight_red%28+2%2F3+%29%29%2Aq+%29=-5%2F3-%281%2F3%29%2Aq-4.
Remove unneeded parentheses around factor highlight_red%28+2+%29,highlight_red%28+1%2F3+%29
It becomes 4%2F3%2Bhighlight_green%28+2+%29%2Fhighlight_green%28+3+%29%2Aq=-5%2F3-%281%2F3%29%2Aq-4.
Look at highlight_red%28+4%2F3+%29%2B2%2F3%2Aq=-5%2F3-%281%2F3%29%2Aq-4.
Moved 4%2F3 to the right of expression
It becomes 2%2F3%2Aq%2Bhighlight_green%28+4%2F3+%29=-5%2F3-%281%2F3%29%2Aq-4.
Look at 2%2F3%2Aq%2B4%2F3=-5%2F3-highlight_red%28+%28highlight_red%28+1%2F3+%29%29%2Aq+%29-4.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F3+%29
It becomes 2%2F3%2Aq%2B4%2F3=-5%2F3-highlight_green%28+1+%29%2Fhighlight_green%28+3+%29%2Aq-4.
Look at 2%2F3%2Aq%2B4%2F3=-5%2F3-highlight_red%28+1+%29%2F3%2Aq-4.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes 2%2F3%2Aq%2B4%2F3=-5%2F3-q%2F3-4.
Look at 2%2F3%2Aq%2B4%2F3=-highlight_red%28+5%2F3+%29-q%2F3-highlight_red%28+4+%29.
Added fractions or integers together
It becomes 2%2F3%2Aq%2B4%2F3=-highlight_green%28+17%2F3+%29-q%2F3.
Look at 2%2F3%2Aq%2B4%2F3=-highlight_red%28+17%2F3+%29-q%2F3.
Moved -17%2F3 to the right of expression
It becomes 2%2F3%2Aq%2B4%2F3=-q%2F3-highlight_green%28+17%2F3+%29.
Look at 2%2F3%2Aq%2B4%2F3=highlight_red%28+-q%2F3-17%2F3+%29.
Moved these terms to the left highlight_green%28+q%2F3+%29,highlight_green%28+17%2F3+%29
It becomes 2%2F3%2Aq%2B4%2F3%2Bhighlight_green%28+q%2F3+%29%2Bhighlight_green%28+17%2F3+%29=0.
Look at 2%2F3%2Aq%2Bhighlight_red%28+4%2F3+%29%2Bq%2F3%2Bhighlight_red%28+17%2F3+%29=0.
Added fractions or integers together
It becomes 2%2F3%2Aq%2Bhighlight_green%28+21%2F3+%29%2Bq%2F3=0.
Look at 2%2F3%2Aq%2Bhighlight_red%28+21%2F3+%29%2Bq%2F3=0.
Moved 21%2F3 to the right of expression
It becomes 2%2F3%2Aq%2Bq%2F3%2Bhighlight_green%28+21%2F3+%29=0.
Look at 2%2F3%2Aq%2Bq%2F3%2Bhighlight_red%28+21+%29%2Fhighlight_red%28+3+%29=0.
Factors 21 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes 2%2F3%2Aq%2Bq%2F3%2Bhighlight_green%28+7+%29%2Fhighlight_green%28+1+%29=0.
Look at 2%2F3%2Aq%2Bq%2F3%2B7%2Fhighlight_red%28+1+%29=0.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 2%2F3%2Aq%2Bq%2F3%2B7=0.
Look at highlight_red%28+2%2F3%2Aq+%29%2Bhighlight_red%28+q%2F3+%29%2B7=0.
Eliminated similar terms highlight_red%28+2%2F3%2Aq+%29,highlight_red%28+q%2F3+%29 replacing them with highlight_green%28+%282%2A1%2F3%2B1%2F3%29%2Aq+%29
It becomes highlight_green%28+%282%2A1%2F3%2B1%2F3%29%2Aq+%29%2B7=0.
Look at highlight_red%28+%282%2A1%2F3%2B1%2F3%29+%29%2Aq%2B7=0.
Remove extraneous '1' from product highlight_red%28+%282%2A1%2F3%2B1%2F3%29+%29
It becomes q%2B7=0.
Look at highlight_red%28+q%2B7+%29=0.
Solved linear equation highlight_red%28+q%2B7=0+%29 equivalent to q+7 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: q=-7.

Universal Simplifier and Solver


Done!