SOLUTION: solve the equation below and show steps in work 1/3(12+x)=-8(6-x)

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Question 941487: solve the equation below and show steps in work
1/3(12+x)=-8(6-x)
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: x=6.78260869565217.
  • Graphical form: Equation %281%2F3%29%2A%2812%2Bx%29=-8%2A%286-x%29 was fully solved.
  • Text form: (1/3)*(12+x)=-8*(6-x) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%281%2F3%29%2A%2812%2Bx%29=-8%2A%286-x%29+%29
    For tutors: simplify_cartoon( (1/3)*(12+x)=-8*(6-x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28highlight_red%28+1%2F3+%29%29%2A%2812%2Bx%29+%29=-8%2A%286-x%29.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F3+%29
It becomes highlight_green%28+1+%29%2Fhighlight_green%28+3+%29%2A%2812%2Bx%29=-8%2A%286-x%29.
Look at highlight_red%28+1+%29%2F3%2A%2812%2Bx%29=-8%2A%286-x%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %2812%2Bx%29%2F3=-8%2A%286-x%29.
Look at %28highlight_red%28+12+%29%2Bx%29%2F3=-8%2A%286-x%29.
Moved 12 to the right of expression
It becomes %28x%2Bhighlight_green%28+12+%29%29%2F3=-8%2A%286-x%29.
Look at %28x%2B12%29%2F3=-8%2A%28highlight_red%28+6+%29-x%29.
Moved 6 to the right of expression
It becomes %28x%2B12%29%2F3=-8%2A%28-x%2Bhighlight_green%28+6+%29%29.
Look at %28x%2B12%29%2F3=highlight_red%28+-8%2A%28-x%2B6%29+%29.
Moved these terms to the left highlight_green%28+8%2A%28-x%2B6%29+%29
It becomes %28x%2B12%29%2F3%2Bhighlight_green%28+8%2A%28-x%2B6%29+%29=0.
Look at highlight_red%28+%28x%2B12%29%2F3+%29%2B8%2A%28-x%2B6%29=0.
Expanded term 1%2F3 by using associative property on %28x%2B12%29
It becomes highlight_green%28+1%2F3%2Ax+%29%2Bhighlight_green%28+1%2F3%2A12+%29%2B8%2A%28-x%2B6%29=0.
Look at highlight_red%28+1+%29%2F3%2Ax%2B1%2F3%2A12%2B8%2A%28-x%2B6%29=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%2F3%2B1%2F3%2A12%2B8%2A%28-x%2B6%29=0.
Look at x%2F3%2B1%2Fhighlight_red%28+3+%29%2Ahighlight_red%28+12+%29%2B8%2A%28-x%2B6%29=0.
Factors 12 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes x%2F3%2B1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+4+%29%2B8%2A%28-x%2B6%29=0.
Look at x%2F3%2Bhighlight_red%28+1+%29%2F1%2Ahighlight_red%28+4+%29%2B8%2A%28-x%2B6%29=0.
Multiplied numerator integers
It becomes x%2F3%2Bhighlight_green%28+4+%29%2F1%2B8%2A%28-x%2B6%29=0.
Look at x%2F3%2Bhighlight_red%28+4%2F1+%29%2B8%2A%28-x%2B6%29=0.
Moved 4%2F1 to the right of expression
It becomes x%2F3%2B8%2A%28-x%2B6%29%2Bhighlight_green%28+4%2F1+%29=0.
Look at x%2F3%2B8%2A%28-x%2B6%29%2B4%2Fhighlight_red%28+1+%29=0.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes x%2F3%2B8%2A%28-x%2B6%29%2B4=0.
Look at x%2F3%2Bhighlight_red%28+8%2A%28-x%2B6%29+%29%2B4=0.
Expanded term 8 by using associative property on %28-x%2B6%29
It becomes x%2F3-highlight_green%28+8%2Ax+%29%2Bhighlight_green%28+8%2A6+%29%2B4=0.
Look at x%2F3-8%2Ax%2Bhighlight_red%28+8+%29%2Ahighlight_red%28+6+%29%2B4=0.
Multiplied numerator integers
It becomes x%2F3-8%2Ax%2Bhighlight_green%28+48+%29%2B4=0.
Look at x%2F3-8%2Ax%2Bhighlight_red%28+48+%29%2Bhighlight_red%28+4+%29=0.
Added fractions or integers together
It becomes x%2F3-8%2Ax%2Bhighlight_green%28+52+%29=0.
Look at highlight_red%28+x%2F3+%29-highlight_red%28+8%2Ax+%29%2B52=0.
Eliminated similar terms highlight_red%28+x%2F3+%29,highlight_red%28+-8%2Ax+%29 replacing them with highlight_green%28+%281%2F3-8%29%2Ax+%29
It becomes highlight_green%28+%281%2F3-8%29%2Ax+%29%2B52=0.
Look at %28highlight_red%28+1%2F3+%29-highlight_red%28+8+%29%29%2Ax%2B52=0.
Added fractions or integers together
It becomes %28-highlight_green%28+23%2F3+%29%29%2Ax%2B52=0.
Look at highlight_red%28+%28-highlight_red%28+23%2F3+%29%29%2Ax+%29%2B52=0.
Remove unneeded parentheses around factor highlight_red%28+23+%29,highlight_red%28+1%2F3+%29
It becomes -highlight_green%28+23+%29%2Fhighlight_green%28+3+%29%2Ax%2B52=0.
Look at highlight_red%28+-23%2F3%2Ax%2B52+%29=0.
Solved linear equation highlight_red%28+-23%2F3%2Ax%2B52=0+%29 equivalent to -7.66666666666667*x+52 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=6.78260869565217.

Universal Simplifier and Solver


Done!

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

solve the equation below and show steps in work
1/3(12+x)=-8(6-x)


%281%2F3%29%2812+%2B+x%29+=+-+8%286+-+x%29

%2812+%2B+x%29%2F3+=+-+8%286+-+x%29

%2812+%2B+x%29%2F3+=+-+48+%2B+8x

3%28-+48+%2B+8x%29+=+12+%2B+x%29 ------- Cross-multiplying

-+144+%2B+24x+=+12+%2B+x%29

24x+-+x+=+12+%2B+144

23x = 156

highlight_green%28x+=+156%2F23%29