SOLUTION: 5(2k + 6) + 2(1 - 3k) = 60

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Question 216456: 5(2k + 6) + 2(1 - 3k) = 60
Found 2 solutions by drj, rfer:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
5%282k+%2B+6%29+%2B+2%281+-+3k%29+=+60+

The following steps will simplify and solve the above equation


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


YOUR ANSWER


  • This is an equation! Solutions: k=7.
  • Graphical form: Equation 5%2A%282k%2B6%29%2B2%2A%281-3k%29=60 was fully solved.
  • Text form: 5*(2k+6)+2*(1-3k)=60 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5%2A%282k%2B6%29%2B2%2A%281-3k%29=60+%29
    For tutors: simplify_cartoon( 5*(2k+6)+2*(1-3k)=60 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2A%282%2Ak%2B6%29%2B2%2A%28highlight_red%28+1+%29-3%2Ak%29=60.
Moved 1 to the right of expression
It becomes 5%2A%282%2Ak%2B6%29%2B2%2A%28-3%2Ak%2Bhighlight_green%28+1+%29%29=60.
Look at 5%2A%282%2Ak%2B6%29%2B2%2A%28-3%2Ak%2B1%29=highlight_red%28+60+%29.
Moved these terms to the left highlight_green%28+-60+%29
It becomes 5%2A%282%2Ak%2B6%29%2B2%2A%28-3%2Ak%2B1%29-highlight_green%28+60+%29=0.
Look at highlight_red%28+5%2A%282%2Ak%2B6%29+%29%2B2%2A%28-3%2Ak%2B1%29-60=0.
Expanded term 5 by using associative property on %282%2Ak%2B6%29
It becomes highlight_green%28+5%2A2%2Ak+%29%2Bhighlight_green%28+5%2A6+%29%2B2%2A%28-3%2Ak%2B1%29-60=0.
Look at highlight_red%28+5+%29%2Ahighlight_red%28+2+%29%2Ak%2B5%2A6%2B2%2A%28-3%2Ak%2B1%29-60=0.
Multiplied numerator integers
It becomes highlight_green%28+10+%29%2Ak%2B5%2A6%2B2%2A%28-3%2Ak%2B1%29-60=0.
Look at 10%2Ak%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+6+%29%2B2%2A%28-3%2Ak%2B1%29-60=0.
Multiplied numerator integers
It becomes 10%2Ak%2Bhighlight_green%28+30+%29%2B2%2A%28-3%2Ak%2B1%29-60=0.
Look at 10%2Ak%2Bhighlight_red%28+30+%29%2B2%2A%28-3%2Ak%2B1%29-highlight_red%28+60+%29=0.
Added fractions or integers together
It becomes 10%2Ak%2Bhighlight_green%28+-30+%29%2B2%2A%28-3%2Ak%2B1%29=0.
Look at 10%2Ak%2Bhighlight_red%28+-30+%29%2B2%2A%28-3%2Ak%2B1%29=0.
Moved -30 to the right of expression
It becomes 10%2Ak%2B2%2A%28-3%2Ak%2B1%29%2Bhighlight_green%28+-30+%29=0.
Look at 10%2Ak%2B2%2A%28-3%2Ak%2B1%29%2Bhighlight_red%28+-30+%29=0.
Removed extra sign in front of -30
It becomes 10%2Ak%2B2%2A%28-3%2Ak%2B1%29-highlight_green%28+30+%29=0.
Look at 10%2Ak%2Bhighlight_red%28+2%2A%28-3%2Ak%2B1%29+%29-30=0.
Expanded term 2 by using associative property on %28-3%2Ak%2B1%29
It becomes 10%2Ak-highlight_green%28+2%2A3%2Ak+%29%2Bhighlight_green%28+2%2A1+%29-30=0.
Look at 10%2Ak-highlight_red%28+2+%29%2Ahighlight_red%28+3+%29%2Ak%2B2%2A1-30=0.
Multiplied numerator integers
It becomes 10%2Ak-highlight_green%28+6+%29%2Ak%2B2%2A1-30=0.
Look at 10%2Ak-6%2Ak%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29-30=0.
Multiplied numerator integers
It becomes 10%2Ak-6%2Ak%2Bhighlight_green%28+2+%29-30=0.
Look at 10%2Ak-6%2Ak%2Bhighlight_red%28+2+%29-highlight_red%28+30+%29=0.
Added fractions or integers together
It becomes 10%2Ak-6%2Ak%2Bhighlight_green%28+-28+%29=0.
Look at 10%2Ak-6%2Ak%2Bhighlight_red%28+-28+%29=0.
Removed extra sign in front of -28
It becomes 10%2Ak-6%2Ak-highlight_green%28+28+%29=0.
Look at highlight_red%28+10%2Ak+%29-highlight_red%28+6%2Ak+%29-28=0.
Eliminated similar terms highlight_red%28+10%2Ak+%29,highlight_red%28+-6%2Ak+%29 replacing them with highlight_green%28+%2810-6%29%2Ak+%29
It becomes highlight_green%28+%2810-6%29%2Ak+%29-28=0.
Look at %28highlight_red%28+10+%29-highlight_red%28+6+%29%29%2Ak-28=0.
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2Ak-28=0.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2Ak+%29-28=0.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2Ak-28=0.
Look at highlight_red%28+4%2Ak-28+%29=0.
Solved linear equation highlight_red%28+4%2Ak-28=0+%29 equivalent to 4*k-28 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: k=7.

Universal Simplifier and Solver


Done!




I hope the above steps and explanation were helpful.

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

Also, good luck in your studies and contact me at
john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
5(2k+6)+2(1-3k)=60
10k+30+2-6k=60
4k=28
k=7