SOLUTION: Given: 2(x+5)=3x+1 Prove: x=9 Supply reasons for each step

Algebra ->  Algebra  -> Geometry-proofs -> SOLUTION: Given: 2(x+5)=3x+1 Prove: x=9 Supply reasons for each step      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 176198: Given: 2(x+5)=3x+1
Prove: x=9
Supply reasons for each step
Found 2 solutions by mathismylife, josmiceli:
Answer by mathismylife(1) About Me  (Show Source):
You can put this solution on YOUR website!
replace the x on both sides with 9, 2(9+5) and 3(9)+1, if you simplify it will be 28=28.

Answer by josmiceli(6785) About Me  (Show Source):
You can put this solution on YOUR website!
As long as you do the same thing to both
sides of the equation,
that is legal in algebra, also the distributive law says
a%28b+%2B+c+%2B+d%29+=+ab+%2B+ac+%2B+ad
To see this, suppose I have
6%2A8+=+48, then suppose I do this:
6%2A%283+%2B+4+%2B+1%29+=+48 Now I say
6%2A3+%2B+6%2A4+%2B+6%2A1+=+48 Is this true?
18+%2B+24+%2B+6+=+48
48+=+48 yes
--------------------
2%28x+%2B+5%29+=+3x+%2B+1 So, I can use distributive law
2x+%2B+10+=+3x+%2B+1
+-2x+=+-2x add -2x to both sides
+0+%2B+10+=+3x+-+2x+%2B+1
10+=+x+%2B+1 add -1 to both sides
10+-+1+=+x+%2B+1+-+1
9+=+x answer