SOLUTION: How do you do these questions I really do need help on these 2(5w-12)=6(-2w+3)+2 1/2(2d-34)=2/3(6d-27) y(y+12)-8y=14+y(y-4) a(a+8)-a(a+3)-23=3a+11

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you do these questions I really do need help on these 2(5w-12)=6(-2w+3)+2 1/2(2d-34)=2/3(6d-27) y(y+12)-8y=14+y(y-4) a(a+8)-a(a+3)-23=3a+11      Log On


   

Question 27324: How do you do these questions I really do need help on these
2(5w-12)=6(-2w+3)+2
1/2(2d-34)=2/3(6d-27)
y(y+12)-8y=14+y(y-4)
a(a+8)-a(a+3)-23=3a+11
Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
2%285w-12%29=6%28-2w%2B3%29%2B2
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: w=2.
  • Graphical form: Equation 2%2A%285w-12%29=6%2A%28-2w%2B3%29%2B2 was fully solved.
  • Text form: 2*(5w-12)=6*(-2w+3)+2 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%285w-12%29=6%2A%28-2w%2B3%29%2B2+%29
    For tutors: simplify_cartoon( 2*(5w-12)=6*(-2w+3)+2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%285%2Aw-12%29=highlight_red%28+6%2A%28-2%2Aw%2B3%29%2B2+%29.
Moved these terms to the left highlight_green%28+-6%2A%28-2%2Aw%2B3%29+%29,highlight_green%28+-2+%29
It becomes 2%2A%285%2Aw-12%29-highlight_green%28+6%2A%28-2%2Aw%2B3%29+%29-highlight_green%28+2+%29=0.
Look at highlight_red%28+2%2A%285%2Aw-12%29+%29-6%2A%28-2%2Aw%2B3%29-2=0.
Expanded term 2 by using associative property on %285%2Aw-12%29
It becomes highlight_green%28+2%2A5%2Aw+%29-highlight_green%28+2%2A12+%29-6%2A%28-2%2Aw%2B3%29-2=0.
Look at highlight_red%28+2+%29%2Ahighlight_red%28+5+%29%2Aw-2%2A12-6%2A%28-2%2Aw%2B3%29-2=0.
Multiplied numerator integers
It becomes highlight_green%28+10+%29%2Aw-2%2A12-6%2A%28-2%2Aw%2B3%29-2=0.
Look at 10%2Aw-highlight_red%28+2+%29%2Ahighlight_red%28+12+%29-6%2A%28-2%2Aw%2B3%29-2=0.
Multiplied numerator integers
It becomes 10%2Aw-highlight_green%28+24+%29-6%2A%28-2%2Aw%2B3%29-2=0.
Look at 10%2Aw-highlight_red%28+24+%29-6%2A%28-2%2Aw%2B3%29-highlight_red%28+2+%29=0.
Added fractions or integers together
It becomes 10%2Aw%2Bhighlight_green%28+-26+%29-6%2A%28-2%2Aw%2B3%29=0.
Look at 10%2Aw%2Bhighlight_red%28+-26+%29-6%2A%28-2%2Aw%2B3%29=0.
Moved -26 to the right of expression
It becomes 10%2Aw-6%2A%28-2%2Aw%2B3%29%2Bhighlight_green%28+-26+%29=0.
Look at 10%2Aw-6%2A%28-2%2Aw%2B3%29%2Bhighlight_red%28+-26+%29=0.
Removed extra sign in front of -26
It becomes 10%2Aw-6%2A%28-2%2Aw%2B3%29-highlight_green%28+26+%29=0.
Look at 10%2Aw-highlight_red%28+6%2A%28-2%2Aw%2B3%29+%29-26=0.
Expanded term -6 by using associative property on %28-2%2Aw%2B3%29
It becomes 10%2Aw%2Bhighlight_green%28+6%2A2%2Aw+%29-highlight_green%28+6%2A3+%29-26=0.
Look at 10%2Aw%2Bhighlight_red%28+6+%29%2Ahighlight_red%28+2+%29%2Aw-6%2A3-26=0.
Multiplied numerator integers
It becomes 10%2Aw%2Bhighlight_green%28+12+%29%2Aw-6%2A3-26=0.
Look at 10%2Aw%2B12%2Aw-highlight_red%28+6+%29%2Ahighlight_red%28+3+%29-26=0.
Multiplied numerator integers
It becomes 10%2Aw%2B12%2Aw-highlight_green%28+18+%29-26=0.
Look at 10%2Aw%2B12%2Aw-highlight_red%28+18+%29-highlight_red%28+26+%29=0.
Added fractions or integers together
It becomes 10%2Aw%2B12%2Aw%2Bhighlight_green%28+-44+%29=0.
Look at 10%2Aw%2B12%2Aw%2Bhighlight_red%28+-44+%29=0.
Removed extra sign in front of -44
It becomes 10%2Aw%2B12%2Aw-highlight_green%28+44+%29=0.
Look at highlight_red%28+10%2Aw+%29%2Bhighlight_red%28+12%2Aw+%29-44=0.
Eliminated similar terms highlight_red%28+10%2Aw+%29,highlight_red%28+12%2Aw+%29 replacing them with highlight_green%28+%2810%2B12%29%2Aw+%29
It becomes highlight_green%28+%2810%2B12%29%2Aw+%29-44=0.
Look at %28highlight_red%28+10+%29%2Bhighlight_red%28+12+%29%29%2Aw-44=0.
Added fractions or integers together
It becomes %28highlight_green%28+22+%29%29%2Aw-44=0.
Look at highlight_red%28+%28highlight_red%28+22+%29%29%2Aw+%29-44=0.
Remove unneeded parentheses around factor highlight_red%28+22+%29
It becomes highlight_green%28+22+%29%2Aw-44=0.
Look at highlight_red%28+22%2Aw-44+%29=0.
Solved linear equation highlight_red%28+22%2Aw-44=0+%29 equivalent to 22*w-44 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=2.

Universal Simplifier and Solver


Done!



%281%2F2%29%282d-34%29=%282%2F3%29%286d-27%29
DISTRIBUTE
d-17=4d-18
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: d=0.333333333333333.
  • Graphical form: Equation d-17=4d-18 was fully solved.
  • Text form: d-17=4d-18 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+d-17=4d-18+%29
    For tutors: simplify_cartoon( d-17=4d-18 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at d-17=highlight_red%28+4%2Ad-18+%29.
Moved these terms to the left highlight_green%28+-4%2Ad+%29,highlight_green%28+18+%29
It becomes d-17-highlight_green%28+4%2Ad+%29%2Bhighlight_green%28+18+%29=0.
Look at d-highlight_red%28+17+%29-4%2Ad%2Bhighlight_red%28+18+%29=0.
Added fractions or integers together
It becomes d%2Bhighlight_green%28+1+%29-4%2Ad=0.
Look at d%2Bhighlight_red%28+1+%29-4%2Ad=0.
Moved 1 to the right of expression
It becomes d-4%2Ad%2Bhighlight_green%28+1+%29=0.
Look at highlight_red%28+d+%29-highlight_red%28+4%2Ad+%29%2B1=0.
Eliminated similar terms highlight_red%28+d+%29,highlight_red%28+-4%2Ad+%29 replacing them with highlight_green%28+%281-4%29%2Ad+%29
It becomes highlight_green%28+%281-4%29%2Ad+%29%2B1=0.
Look at %28highlight_red%28+1+%29-highlight_red%28+4+%29%29%2Ad%2B1=0.
Added fractions or integers together
It becomes %28highlight_green%28+-3+%29%29%2Ad%2B1=0.
Look at %28highlight_red%28+-3+%29%29%2Ad%2B1=0.
Removed extra sign in front of -3
It becomes %28-highlight_green%28+3+%29%29%2Ad%2B1=0.
Look at highlight_red%28+%28-highlight_red%28+3+%29%29%2Ad+%29%2B1=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes -highlight_green%28+3+%29%2Ad%2B1=0.
Look at highlight_red%28+-3%2Ad%2B1+%29=0.
Solved linear equation highlight_red%28+-3%2Ad%2B1=0+%29 equivalent to -3*d+1 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: d=0.333333333333333.

Universal Simplifier and Solver


Done!



y%28y%2B12%29-8y=14%2By%28y-4%29
DISTRIBUTE
y%5E2%2B12y-8y=14%2By%5E2-4y
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: y=1.75.
  • Graphical form: Equation y%5E2%2B12y-8y=14%2By%5E2-4y was fully solved.
  • Text form: y^2+12y-8y=14+y^2-4y simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+y%5E2%2B12y-8y=14%2By%5E2-4y+%29
    For tutors: simplify_cartoon( y^2+12y-8y=14+y^2-4y )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at y%5E2%2Bhighlight_red%28+12%2Ay+%29-highlight_red%28+8%2Ay+%29=14%2By%5E2-4y.
Eliminated similar terms highlight_red%28+12%2Ay+%29,highlight_red%28+-8%2Ay+%29 replacing them with highlight_green%28+%2812-8%29%2Ay+%29
It becomes y%5E2%2Bhighlight_green%28+%2812-8%29%2Ay+%29=14%2By%5E2-4y.
Look at y%5E2%2B%28highlight_red%28+12+%29-highlight_red%28+8+%29%29%2Ay=14%2By%5E2-4y.
Added fractions or integers together
It becomes y%5E2%2B%28highlight_green%28+4+%29%29%2Ay=14%2By%5E2-4y.
Look at y%5E2%2Bhighlight_red%28+%28highlight_red%28+4+%29%29%2Ay+%29=14%2By%5E2-4y.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes y%5E2%2Bhighlight_green%28+4+%29%2Ay=14%2By%5E2-4y.
Look at y%5E2%2B4%2Ay=highlight_red%28+14+%29%2By%5E2-4%2Ay.
Moved 14 to the right of expression
It becomes y%5E2%2B4%2Ay=y%5E2-4%2Ay%2Bhighlight_green%28+14+%29.
Look at y%5E2%2B4%2Ay=highlight_red%28+y%5E2-4%2Ay%2B14+%29.
Moved these terms to the left highlight_green%28+-y%5E2+%29,highlight_green%28+4%2Ay+%29,highlight_green%28+-14+%29
It becomes .
Look at highlight_red%28+y%5E2+%29%2B4%2Ay-highlight_red%28+y%5E2+%29%2B4%2Ay-14=0.
Eliminated similar terms highlight_red%28+y%5E2+%29,highlight_red%28+-y%5E2+%29 replacing them with highlight_green%28+%281-1%29%2Ay%5E2+%29
It becomes highlight_green%28+%281-1%29%2Ay%5E2+%29%2B4%2Ay%2B4%2Ay-14=0.
Look at %281-1%29%2Ay%5E2%2Bhighlight_red%28+4%2Ay+%29%2Bhighlight_red%28+4%2Ay+%29-14=0.
Eliminated similar terms highlight_red%28+4%2Ay+%29,highlight_red%28+4%2Ay+%29 replacing them with highlight_green%28+%284%2B4%29%2Ay+%29
It becomes %281-1%29%2Ay%5E2%2Bhighlight_green%28+%284%2B4%29%2Ay+%29-14=0.
Look at highlight_red%28+%281-1%29%2Ay%5E2+%29%2B%284%2B4%29%2Ay-14=0.
Since highlight_red%28+%281-1%29%2Ay%5E2+%29 has zero as a factor, it should be replaced with a zero
Look at 0%2B%284%2B4%29%2Ay-14=0.
Added fractions or integers together
It becomes 0%2B%284%2B4%29%2Ay-14=0.
Look at 0%2B%28highlight_red%28+4+%29%2Bhighlight_red%28+4+%29%29%2Ay-14=0.
Added fractions or integers together
It becomes 0%2B%28highlight_green%28+8+%29%29%2Ay-14=0.
Look at highlight_red%28+0+%29%2B%288%29%2Ay-14=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes %288%29%2Ay-14=0.
Look at highlight_red%28+%28highlight_red%28+8+%29%29%2Ay+%29-14=0.
Remove unneeded parentheses around factor highlight_red%28+8+%29
It becomes highlight_green%28+8+%29%2Ay-14=0.
Look at highlight_red%28+8%2Ay-14+%29=0.
Solved linear equation highlight_red%28+8%2Ay-14=0+%29 equivalent to 8*y-14 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=1.75.

Universal Simplifier and Solver


Done!



a%28a%2B8%29-a%28a%2B3%29-23=3a%2B11
DISTRIBUTE
a%5E2+%2B8a-a%5E2-3a-23=3a%2B11
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: a=17.
  • Graphical form: Equation a%5E2%2B8a-a%5E2-3a-23=3a%2B11 was fully solved.
  • Text form: a^2+8a-a^2-3a-23=3a+11 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+a%5E2%2B8a-a%5E2-3a-23=3a%2B11+%29
    For tutors: simplify_cartoon( a^2+8a-a^2-3a-23=3a+11 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+a%5E2+%29%2B8%2Aa-highlight_red%28+a%5E2+%29-3%2Aa-23=3a%2B11.
Eliminated similar terms highlight_red%28+a%5E2+%29,highlight_red%28+-a%5E2+%29 replacing them with highlight_green%28+%281-1%29%2Aa%5E2+%29
It becomes highlight_green%28+%281-1%29%2Aa%5E2+%29%2B8%2Aa-3%2Aa-23=3a%2B11.
Look at %281-1%29%2Aa%5E2%2Bhighlight_red%28+8%2Aa+%29-highlight_red%28+3%2Aa+%29-23=3a%2B11.
Eliminated similar terms highlight_red%28+8%2Aa+%29,highlight_red%28+-3%2Aa+%29 replacing them with highlight_green%28+%288-3%29%2Aa+%29
It becomes %281-1%29%2Aa%5E2%2Bhighlight_green%28+%288-3%29%2Aa+%29-23=3a%2B11.
Look at highlight_red%28+%281-1%29%2Aa%5E2+%29%2B%288-3%29%2Aa-23=3a%2B11.
Since highlight_red%28+%281-1%29%2Aa%5E2+%29 has zero as a factor, it should be replaced with a zero
Look at 0%2B%288-3%29%2Aa-23=3a%2B11.
Added fractions or integers together
It becomes 0%2B%288-3%29%2Aa-23=3a%2B11.
Look at 0%2B%28highlight_red%28+8+%29-highlight_red%28+3+%29%29%2Aa-23=3a%2B11.
Added fractions or integers together
It becomes 0%2B%28highlight_green%28+5+%29%29%2Aa-23=3a%2B11.
Look at highlight_red%28+0+%29%2B%285%29%2Aa-23=3a%2B11.
Remove extraneous zero highlight_red%28+0+%29
It becomes %285%29%2Aa-23=3a%2B11.
Look at highlight_red%28+%28highlight_red%28+5+%29%29%2Aa+%29-23=3a%2B11.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes highlight_green%28+5+%29%2Aa-23=3a%2B11.
Look at 5%2Aa-23=highlight_red%28+3%2Aa%2B11+%29.
Moved these terms to the left highlight_green%28+-3%2Aa+%29,highlight_green%28+-11+%29
It becomes 5%2Aa-23-highlight_green%28+3%2Aa+%29-highlight_green%28+11+%29=0.
Look at 5%2Aa-highlight_red%28+23+%29-3%2Aa-highlight_red%28+11+%29=0.
Added fractions or integers together
It becomes 5%2Aa%2Bhighlight_green%28+-34+%29-3%2Aa=0.
Look at 5%2Aa%2Bhighlight_red%28+-34+%29-3%2Aa=0.
Moved -34 to the right of expression
It becomes 5%2Aa-3%2Aa%2Bhighlight_green%28+-34+%29=0.
Look at 5%2Aa-3%2Aa%2Bhighlight_red%28+-34+%29=0.
Removed extra sign in front of -34
It becomes 5%2Aa-3%2Aa-highlight_green%28+34+%29=0.
Look at highlight_red%28+5%2Aa+%29-highlight_red%28+3%2Aa+%29-34=0.
Eliminated similar terms highlight_red%28+5%2Aa+%29,highlight_red%28+-3%2Aa+%29 replacing them with highlight_green%28+%285-3%29%2Aa+%29
It becomes highlight_green%28+%285-3%29%2Aa+%29-34=0.
Look at %28highlight_red%28+5+%29-highlight_red%28+3+%29%29%2Aa-34=0.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2Aa-34=0.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2Aa+%29-34=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2Aa-34=0.
Look at highlight_red%28+2%2Aa-34+%29=0.
Solved linear equation highlight_red%28+2%2Aa-34=0+%29 equivalent to 2*a-34 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=17.

Universal Simplifier and Solver


Done!


Hope this helps!