SOLUTION: the sum of of four times a number and three is the same as the difference of twice the number and eleven.find the number

Algebra ->  Customizable Word Problem Solvers  -> Unit conversion -> SOLUTION: the sum of of four times a number and three is the same as the difference of twice the number and eleven.find the number      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 223711: the sum of of four times a number and three is the same as the difference of twice the number and eleven.find the number
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The the sum of of four times a number and three is the same as the difference of twice the number and eleven. Find the number.

Step 1. Let x be a number

Step 2. Let 4x+3 be the sum of four times a number and three.

Step 3. Let 2x-11 be the difference of twice the number and eleven.

Step 4. Set Steps 2 and 3 to be equal: 4x%2B3=2x-11 since the the sum of of four times a number and three is the same as the difference of twice the number and eleven.

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


YOUR ANSWER


  • This is an equation! Solutions: x=-7.
  • Graphical form: Equation 4x%2B3=2x-11 was fully solved.
  • Text form: 4x+3=2x-11 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4x%2B3=2x-11+%29
    For tutors: simplify_cartoon( 4x+3=2x-11 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Ax%2B3=highlight_red%28+2%2Ax-11+%29.
Moved these terms to the left highlight_green%28+-2%2Ax+%29,highlight_green%28+11+%29
It becomes 4%2Ax%2B3-highlight_green%28+2%2Ax+%29%2Bhighlight_green%28+11+%29=0.
Look at 4%2Ax%2Bhighlight_red%28+3+%29-2%2Ax%2Bhighlight_red%28+11+%29=0.
Added fractions or integers together
It becomes 4%2Ax%2Bhighlight_green%28+14+%29-2%2Ax=0.
Look at 4%2Ax%2Bhighlight_red%28+14+%29-2%2Ax=0.
Moved 14 to the right of expression
It becomes 4%2Ax-2%2Ax%2Bhighlight_green%28+14+%29=0.
Look at highlight_red%28+4%2Ax+%29-highlight_red%28+2%2Ax+%29%2B14=0.
Eliminated similar terms highlight_red%28+4%2Ax+%29,highlight_red%28+-2%2Ax+%29 replacing them with highlight_green%28+%284-2%29%2Ax+%29
It becomes highlight_green%28+%284-2%29%2Ax+%29%2B14=0.
Look at %28highlight_red%28+4+%29-highlight_red%28+2+%29%29%2Ax%2B14=0.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2Ax%2B14=0.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2Ax+%29%2B14=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2Ax%2B14=0.
Look at highlight_red%28+2%2Ax%2B14+%29=0.
Solved linear equation highlight_red%28+2%2Ax%2B14=0+%29 equivalent to 2*x+14 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-7.

Universal Simplifier and Solver


Done!



Step 5. ANSWER: The number is -7.

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