SOLUTION: One number is 8 less than another number. Find the numbers if three times the smaller number is six less than two times the larger number

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Question 215304: One number is 8 less than another number. Find the numbers if three times the smaller number is six less than two times the larger number
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
One number is 8 less than another number. Find the numbers if three times the smaller number is six less than two times the larger number

Step 1. Let x be the smaller number and x+8 be the larger number

Step 2. Let 3x be three times the smaller number.

Step 3. Let 2(x+8) be two times the larger number.

Step 4. Since three times the smaller number is six less than two times the larger number, then 3x=2%28x%2B8%29-6

Step 5. Solving the equation in Step 4 yields the following steps.

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


YOUR ANSWER


  • This is an equation! Solutions: x=10.
  • Graphical form: Equation 3x=2%2A%28x%2B8%29-6 was fully solved.
  • Text form: 3x=2*(x+8)-6 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3x=2%2A%28x%2B8%29-6+%29
    For tutors: simplify_cartoon( 3x=2*(x+8)-6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2Ax=highlight_red%28+2%2A%28x%2B8%29-6+%29.
Moved these terms to the left highlight_green%28+-2%2A%28x%2B8%29+%29,highlight_green%28+6+%29
It becomes 3%2Ax-highlight_green%28+2%2A%28x%2B8%29+%29%2Bhighlight_green%28+6+%29=0.
Look at 3%2Ax-highlight_red%28+2%2A%28x%2B8%29+%29%2B6=0.
Expanded term -2 by using associative property on %28x%2B8%29
It becomes 3%2Ax-highlight_green%28+2%2Ax+%29-highlight_green%28+2%2A8+%29%2B6=0.
Look at 3%2Ax-2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+8+%29%2B6=0.
Multiplied numerator integers
It becomes 3%2Ax-2%2Ax-highlight_green%28+16+%29%2B6=0.
Look at 3%2Ax-2%2Ax-highlight_red%28+16+%29%2Bhighlight_red%28+6+%29=0.
Added fractions or integers together
It becomes 3%2Ax-2%2Ax%2Bhighlight_green%28+-10+%29=0.
Look at 3%2Ax-2%2Ax%2Bhighlight_red%28+-10+%29=0.
Removed extra sign in front of -10
It becomes 3%2Ax-2%2Ax-highlight_green%28+10+%29=0.
Look at highlight_red%28+3%2Ax+%29-highlight_red%28+2%2Ax+%29-10=0.
Eliminated similar terms highlight_red%28+3%2Ax+%29,highlight_red%28+-2%2Ax+%29 replacing them with highlight_green%28+%283-2%29%2Ax+%29
It becomes highlight_green%28+%283-2%29%2Ax+%29-10=0.
Look at highlight_red%28+%283-2%29+%29%2Ax-10=0.
Remove extraneous '1' from product highlight_red%28+%283-2%29+%29
It becomes x-10=0.
Look at highlight_red%28+x-10+%29=0.
Solved linear equation highlight_red%28+x-10=0+%29 equivalent to x-10 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=10.

Universal Simplifier and Solver


Done!



With x=10 , then x+8=18

Step 6. ANSWER: The numbers are 10 and 18.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J