SOLUTION: -3(x+5)=3(x-1) 6-b=5b+30 5y-2y=3y+2 2(7+3t)=-t 3(a+1)-5=3a-2

Algebra ->  Systems-of-equations -> SOLUTION: -3(x+5)=3(x-1) 6-b=5b+30 5y-2y=3y+2 2(7+3t)=-t 3(a+1)-5=3a-2      Log On


   

Question 27359: -3(x+5)=3(x-1)
6-b=5b+30
5y-2y=3y+2
2(7+3t)=-t
3(a+1)-5=3a-2
Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
-3%28x%2B5%29=3%28x-1%29
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=-2.
  • Graphical form: Equation -3%2A%28x%2B5%29=3%2A%28x-1%29 was fully solved.
  • Text form: -3*(x+5)=3*(x-1) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-3%2A%28x%2B5%29=3%2A%28x-1%29+%29
    For tutors: simplify_cartoon( -3*(x+5)=3*(x-1) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -3%2A%28x%2B5%29=highlight_red%28+3%2A%28x-1%29+%29.
Moved these terms to the left highlight_green%28+-3%2A%28x-1%29+%29
It becomes -3%2A%28x%2B5%29-highlight_green%28+3%2A%28x-1%29+%29=0.
Look at -highlight_red%28+3%2A%28x%2B5%29+%29-3%2A%28x-1%29=0.
Expanded term -3 by using associative property on %28x%2B5%29
It becomes -highlight_green%28+3%2Ax+%29-highlight_green%28+3%2A5+%29-3%2A%28x-1%29=0.
Look at -3%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+5+%29-3%2A%28x-1%29=0.
Multiplied numerator integers
It becomes -3%2Ax-highlight_green%28+15+%29-3%2A%28x-1%29=0.
Look at -3%2Ax-highlight_red%28+15+%29-3%2A%28x-1%29=0.
Moved -15 to the right of expression
It becomes -3%2Ax-3%2A%28x-1%29-highlight_green%28+15+%29=0.
Look at -3%2Ax-highlight_red%28+3%2A%28x-1%29+%29-15=0.
Expanded term -3 by using associative property on %28x-1%29
It becomes -3%2Ax-highlight_green%28+3%2Ax+%29%2Bhighlight_green%28+3%2A1+%29-15=0.
Look at -3%2Ax-3%2Ax%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29-15=0.
Multiplied numerator integers
It becomes -3%2Ax-3%2Ax%2Bhighlight_green%28+3+%29-15=0.
Look at -3%2Ax-3%2Ax%2Bhighlight_red%28+3+%29-highlight_red%28+15+%29=0.
Added fractions or integers together
It becomes -3%2Ax-3%2Ax%2Bhighlight_green%28+-12+%29=0.
Look at -3%2Ax-3%2Ax%2Bhighlight_red%28+-12+%29=0.
Removed extra sign in front of -12
It becomes -3%2Ax-3%2Ax-highlight_green%28+12+%29=0.
Look at -highlight_red%28+3%2Ax+%29-highlight_red%28+3%2Ax+%29-12=0.
Eliminated similar terms highlight_red%28+-3%2Ax+%29,highlight_red%28+-3%2Ax+%29 replacing them with highlight_green%28+%28-3-3%29%2Ax+%29
It becomes highlight_green%28+%28-3-3%29%2Ax+%29-12=0.
Look at %28-highlight_red%28+3+%29-highlight_red%28+3+%29%29%2Ax-12=0.
Added fractions or integers together
It becomes %28highlight_green%28+-6+%29%29%2Ax-12=0.
Look at %28highlight_red%28+-6+%29%29%2Ax-12=0.
Removed extra sign in front of -6
It becomes %28-highlight_green%28+6+%29%29%2Ax-12=0.
Look at highlight_red%28+%28-highlight_red%28+6+%29%29%2Ax+%29-12=0.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes -highlight_green%28+6+%29%2Ax-12=0.
Look at highlight_red%28+-6%2Ax-12+%29=0.
Solved linear equation highlight_red%28+-6%2Ax-12=0+%29 equivalent to -6*x-12 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-2.

Universal Simplifier and Solver


Done!



6-b=5b%2B30
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: b=-4.
  • Graphical form: Equation 6-b=5b%2B30 was fully solved.
  • Text form: 6-b=5b+30 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+6-b=5b%2B30+%29
    For tutors: simplify_cartoon( 6-b=5b+30 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+6+%29-b=5b%2B30.
Moved 6 to the right of expression
It becomes -b%2Bhighlight_green%28+6+%29=5b%2B30.
Look at -b%2B6=highlight_red%28+5%2Ab%2B30+%29.
Moved these terms to the left highlight_green%28+-5%2Ab+%29,highlight_green%28+-30+%29
It becomes -b%2B6-highlight_green%28+5%2Ab+%29-highlight_green%28+30+%29=0.
Look at -b%2Bhighlight_red%28+6+%29-5%2Ab-highlight_red%28+30+%29=0.
Added fractions or integers together
It becomes -b%2Bhighlight_green%28+-24+%29-5%2Ab=0.
Look at -b%2Bhighlight_red%28+-24+%29-5%2Ab=0.
Moved -24 to the right of expression
It becomes -b-5%2Ab%2Bhighlight_green%28+-24+%29=0.
Look at -b-5%2Ab%2Bhighlight_red%28+-24+%29=0.
Removed extra sign in front of -24
It becomes -b-5%2Ab-highlight_green%28+24+%29=0.
Look at -highlight_red%28+b+%29-highlight_red%28+5%2Ab+%29-24=0.
Eliminated similar terms highlight_red%28+-b+%29,highlight_red%28+-5%2Ab+%29 replacing them with highlight_green%28+%28-1-5%29%2Ab+%29
It becomes highlight_green%28+%28-1-5%29%2Ab+%29-24=0.
Look at %28-highlight_red%28+1+%29-highlight_red%28+5+%29%29%2Ab-24=0.
Added fractions or integers together
It becomes %28highlight_green%28+-6+%29%29%2Ab-24=0.
Look at %28highlight_red%28+-6+%29%29%2Ab-24=0.
Removed extra sign in front of -6
It becomes %28-highlight_green%28+6+%29%29%2Ab-24=0.
Look at highlight_red%28+%28-highlight_red%28+6+%29%29%2Ab+%29-24=0.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes -highlight_green%28+6+%29%2Ab-24=0.
Look at highlight_red%28+-6%2Ab-24+%29=0.
Solved linear equation highlight_red%28+-6%2Ab-24=0+%29 equivalent to -6*b-24 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: b=-4.

Universal Simplifier and Solver


Done!



5y-2y=3y%2B2
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: 5y-2y=3y%2B2 simplifies to -2=0
  • Text form: 5y-2y=3y+2 simplifies to -2=0
  • Cartoon (animation) form: simplify_cartoon%28+5y-2y=3y%2B2+%29
    For tutors: simplify_cartoon( 5y-2y=3y+2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+5%2Ay+%29-highlight_red%28+2%2Ay+%29=3y%2B2.
Eliminated similar terms highlight_red%28+5%2Ay+%29,highlight_red%28+-2%2Ay+%29 replacing them with highlight_green%28+%285-2%29%2Ay+%29
It becomes highlight_green%28+%285-2%29%2Ay+%29=3y%2B2.
Look at %28highlight_red%28+5+%29-highlight_red%28+2+%29%29%2Ay=3y%2B2.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ay=3y%2B2.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ay+%29=3y%2B2.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ay=3y%2B2.
Look at 3%2Ay=highlight_red%28+3%2Ay%2B2+%29.
Moved these terms to the left highlight_green%28+-3%2Ay+%29,highlight_green%28+-2+%29
It becomes 3%2Ay-highlight_green%28+3%2Ay+%29-highlight_green%28+2+%29=0.
Look at highlight_red%28+3%2Ay+%29-highlight_red%28+3%2Ay+%29-2=0.
Eliminated similar terms highlight_red%28+3%2Ay+%29,highlight_red%28+-3%2Ay+%29 replacing them with highlight_green%28+%283-3%29%2Ay+%29
It becomes highlight_green%28+%283-3%29%2Ay+%29-2=0.
Look at highlight_red%28+%283-3%29%2Ay+%29-2=0.
Since highlight_red%28+%283-3%29%2Ay+%29 has zero as a factor, it should be replaced with a zero
Look at 0-2=0.
Added fractions or integers together
It becomes 0-2=0.
Look at highlight_red%28+0+%29-2=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes -2=0.
Result: -2=0

Universal Simplifier and Solver


Done!



2%287%2B3t%29=-t
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: t=-2.
  • Graphical form: Equation 2%2A%287%2B3t%29=-t was fully solved.
  • Text form: 2*(7+3t)=-t simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%287%2B3t%29=-t+%29
    For tutors: simplify_cartoon( 2*(7+3t)=-t )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%28highlight_red%28+7+%29%2B3%2At%29=-t.
Moved 7 to the right of expression
It becomes 2%2A%283%2At%2Bhighlight_green%28+7+%29%29=-t.
Look at 2%2A%283%2At%2B7%29=highlight_red%28+-t+%29.
Moved these terms to the left highlight_green%28+t+%29
It becomes 2%2A%283%2At%2B7%29%2Bhighlight_green%28+t+%29=0.
Look at highlight_red%28+2%2A%283%2At%2B7%29+%29%2Bt=0.
Expanded term 2 by using associative property on %283%2At%2B7%29
It becomes highlight_green%28+2%2A3%2At+%29%2Bhighlight_green%28+2%2A7+%29%2Bt=0.
Look at highlight_red%28+2+%29%2Ahighlight_red%28+3+%29%2At%2B2%2A7%2Bt=0.
Multiplied numerator integers
It becomes highlight_green%28+6+%29%2At%2B2%2A7%2Bt=0.
Look at 6%2At%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+7+%29%2Bt=0.
Multiplied numerator integers
It becomes 6%2At%2Bhighlight_green%28+14+%29%2Bt=0.
Look at 6%2At%2Bhighlight_red%28+14+%29%2Bt=0.
Moved 14 to the right of expression
It becomes 6%2At%2Bt%2Bhighlight_green%28+14+%29=0.
Look at highlight_red%28+6%2At+%29%2Bhighlight_red%28+t+%29%2B14=0.
Eliminated similar terms highlight_red%28+6%2At+%29,highlight_red%28+t+%29 replacing them with highlight_green%28+%286%2B1%29%2At+%29
It becomes highlight_green%28+%286%2B1%29%2At+%29%2B14=0.
Look at %28highlight_red%28+6+%29%2Bhighlight_red%28+1+%29%29%2At%2B14=0.
Added fractions or integers together
It becomes %28highlight_green%28+7+%29%29%2At%2B14=0.
Look at highlight_red%28+%28highlight_red%28+7+%29%29%2At+%29%2B14=0.
Remove unneeded parentheses around factor highlight_red%28+7+%29
It becomes highlight_green%28+7+%29%2At%2B14=0.
Look at highlight_red%28+7%2At%2B14+%29=0.
Solved linear equation highlight_red%28+7%2At%2B14=0+%29 equivalent to 7*t+14 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: t=-2.

Universal Simplifier and Solver


Done!



3%28a%2B1%29-5=3a-2
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: Equation 3%2A%28a%2B1%29-5=3a-2 was fully solved.
  • Text form: 3*(a+1)-5=3a-2 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3%2A%28a%2B1%29-5=3a-2+%29
    For tutors: simplify_cartoon( 3*(a+1)-5=3a-2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2A%28a%2B1%29-5=highlight_red%28+3%2Aa-2+%29.
Moved these terms to the left highlight_green%28+-3%2Aa+%29,highlight_green%28+2+%29
It becomes 3%2A%28a%2B1%29-5-highlight_green%28+3%2Aa+%29%2Bhighlight_green%28+2+%29=0.
Look at 3%2A%28a%2B1%29-highlight_red%28+5+%29-3%2Aa%2Bhighlight_red%28+2+%29=0.
Added fractions or integers together
It becomes 3%2A%28a%2B1%29%2Bhighlight_green%28+-3+%29-3%2Aa=0.
Look at 3%2A%28a%2B1%29%2Bhighlight_red%28+-3+%29-3%2Aa=0.
Moved -3 to the right of expression
It becomes 3%2A%28a%2B1%29-3%2Aa%2Bhighlight_green%28+-3+%29=0.
Look at 3%2A%28a%2B1%29-3%2Aa%2Bhighlight_red%28+-3+%29=0.
Removed extra sign in front of -3
It becomes 3%2A%28a%2B1%29-3%2Aa-highlight_green%28+3+%29=0.
Look at highlight_red%28+3%2A%28a%2B1%29+%29-3%2Aa-3=0.
Expanded term 3 by using associative property on %28a%2B1%29
It becomes highlight_green%28+3%2Aa+%29%2Bhighlight_green%28+3%2A1+%29-3%2Aa-3=0.
Look at 3%2Aa%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29-3%2Aa-3=0.
Multiplied numerator integers
It becomes 3%2Aa%2Bhighlight_green%28+3+%29-3%2Aa-3=0.
Look at 3%2Aa%2Bhighlight_red%28+3+%29-3%2Aa-highlight_red%28+3+%29=0.
Added fractions or integers together
It becomes 3%2Aa%2Bhighlight_green%28+0+%29-3%2Aa=0.
Look at 3%2Aa%2Bhighlight_red%28+0+%29-3%2Aa=0.
Moved 0 to the right of expression
It becomes 3%2Aa-3%2Aa%2Bhighlight_green%28+0+%29=0.
Look at 3%2Aa-3%2Aa%2Bhighlight_red%28+0+%29=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes 3%2Aa-3%2Aa=0.
Look at highlight_red%28+3%2Aa+%29-highlight_red%28+3%2Aa+%29=0.
Eliminated similar terms highlight_red%28+3%2Aa+%29,highlight_red%28+-3%2Aa+%29 replacing them with highlight_green%28+%283-3%29%2Aa+%29
It becomes highlight_green%28+%283-3%29%2Aa+%29=0.
Look at highlight_red%28+%283-3%29%2Aa+%29=0.
Since highlight_red%28+%283-3%29%2Aa+%29 has zero as a factor, it should be replaced with a zero
Look at 0=0.
Added fractions or integers together
It becomes 0=0.
Result: 0=0

Universal Simplifier and Solver


Done!



Next time, please separate your questions. Thanks. :)
Hope this helps!