SOLUTION: How do I solve this problem 4(x-6)-7((x-2)=17

Algebra ->  Expressions -> SOLUTION: How do I solve this problem 4(x-6)-7((x-2)=17      Log On


   

Question 18737: How do I solve this problem 4(x-6)-7((x-2)=17
Found 2 solutions by pwac, Alwayscheerful:
Answer by pwac(253) About Me  (Show Source):
You can put this solution on YOUR website!
How do I solve this problem 4(x-6)-7((x-2)=17
first deal with brackets,multiply by number in front
taking note of the signs
4x-24-7x+14=17 rearrange taking numbers to right
4x-7x=17+24-14 (again note sign changes as side changes)
-3x=27 divide both sides by -3
x=-9
Pete

Answer by Alwayscheerful(414) 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=-9.
  • Graphical form: Equation 4%2A%28x-6%29-7%2A%28x-2%29=17 was fully solved.
  • Text form: 4*(x-6)-7*(x-2)=17 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4%2A%28x-6%29-7%2A%28x-2%29=17+%29
    For tutors: simplify_cartoon( 4*(x-6)-7*(x-2)=17 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2A%28x-6%29-7%2A%28x-2%29=highlight_red%28+17+%29.
Moved these terms to the left highlight_green%28+-17+%29
It becomes 4%2A%28x-6%29-7%2A%28x-2%29-highlight_green%28+17+%29=0.
Look at highlight_red%28+4%2A%28x-6%29+%29-7%2A%28x-2%29-17=0.
Expanded term 4 by using associative property on %28x-6%29
It becomes highlight_green%28+4%2Ax+%29-highlight_green%28+4%2A6+%29-7%2A%28x-2%29-17=0.
Look at 4%2Ax-highlight_red%28+4+%29%2Ahighlight_red%28+6+%29-7%2A%28x-2%29-17=0.
Multiplied numerator integers
It becomes 4%2Ax-highlight_green%28+24+%29-7%2A%28x-2%29-17=0.
Look at 4%2Ax-highlight_red%28+24+%29-7%2A%28x-2%29-highlight_red%28+17+%29=0.
Added fractions or integers together
It becomes 4%2Ax%2Bhighlight_green%28+-41+%29-7%2A%28x-2%29=0.
Look at 4%2Ax%2Bhighlight_red%28+-41+%29-7%2A%28x-2%29=0.
Moved -41 to the right of expression
It becomes 4%2Ax-7%2A%28x-2%29%2Bhighlight_green%28+-41+%29=0.
Look at 4%2Ax-7%2A%28x-2%29%2Bhighlight_red%28+-41+%29=0.
Removed extra sign in front of -41
It becomes 4%2Ax-7%2A%28x-2%29-highlight_green%28+41+%29=0.
Look at 4%2Ax-highlight_red%28+7%2A%28x-2%29+%29-41=0.
Expanded term -7 by using associative property on %28x-2%29
It becomes 4%2Ax-highlight_green%28+7%2Ax+%29%2Bhighlight_green%28+7%2A2+%29-41=0.
Look at 4%2Ax-7%2Ax%2Bhighlight_red%28+7+%29%2Ahighlight_red%28+2+%29-41=0.
Multiplied numerator integers
It becomes 4%2Ax-7%2Ax%2Bhighlight_green%28+14+%29-41=0.
Look at 4%2Ax-7%2Ax%2Bhighlight_red%28+14+%29-highlight_red%28+41+%29=0.
Added fractions or integers together
It becomes 4%2Ax-7%2Ax%2Bhighlight_green%28+-27+%29=0.
Look at 4%2Ax-7%2Ax%2Bhighlight_red%28+-27+%29=0.
Removed extra sign in front of -27
It becomes 4%2Ax-7%2Ax-highlight_green%28+27+%29=0.
Look at highlight_red%28+4%2Ax+%29-highlight_red%28+7%2Ax+%29-27=0.
Eliminated similar terms highlight_red%28+4%2Ax+%29,highlight_red%28+-7%2Ax+%29 replacing them with highlight_green%28+%284-7%29%2Ax+%29
It becomes highlight_green%28+%284-7%29%2Ax+%29-27=0.
Look at %28highlight_red%28+4+%29-highlight_red%28+7+%29%29%2Ax-27=0.
Added fractions or integers together
It becomes %28highlight_green%28+-3+%29%29%2Ax-27=0.
Look at %28highlight_red%28+-3+%29%29%2Ax-27=0.
Removed extra sign in front of -3
It becomes %28-highlight_green%28+3+%29%29%2Ax-27=0.
Look at highlight_red%28+%28-highlight_red%28+3+%29%29%2Ax+%29-27=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes -highlight_green%28+3+%29%2Ax-27=0.
Look at highlight_red%28+-3%2Ax-27+%29=0.
Solved linear equation highlight_red%28+-3%2Ax-27=0+%29 equivalent to -3*x-27 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-9.

Universal Simplifier and Solver


Done!

Hope this helps!