SOLUTION: simplify 1. 2z+1/3z-z-6/5z solve 1. 5b^2-15b=0

Algebra ->  Expressions -> SOLUTION: simplify 1. 2z+1/3z-z-6/5z solve 1. 5b^2-15b=0       Log On


   

Question 174203: simplify
1. 2z+1/3z-z-6/5z
solve
1. 5b^2-15b=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

Problem:

simplify
1. 2z+1/3z-z-6/5z



Solution:


%282z%2B1%29%2F%283z%29-%28z-6%29%2F%285z%29 Start with the given expression.


%285%2F5%29%28%282z%2B1%29%2F%283z%29%29-%28z-6%29%2F%285z%29 Multiply the 1st fraction %282z%2B1%29%2F%283z%29 by 5%2F5


%285%282z%2B1%29%29%2F%285%283z%29%29-%28z-6%29%2F%285z%29 Combine the fractions.


%2810z%2B5%29%2F%285%283z%29%29-%28z-6%29%2F%285z%29 Distribute


%2810z%2B5%29%2F%2815z%29-%28z-6%29%2F%285z%29 Multiply


%2810z%2B5%29%2F%2815z%29-%283%2F3%29%28%28z-6%29%2F%285z%29%29 Multiply the 2nd fraction %28z-6%29%2F%285z%29 by 3%2F3




%2810z%2B5%29%2F%2815z%29-%283%28z-6%29%29%2F%283%285z%29%29 Combine the fractions.


%2810z%2B5%29%2F%2815z%29-%283z-18%29%2F%283%285z%29%29 Distribute.


%2810z%2B5%29%2F%2815z%29-%283z-18%29%2F%2815z%29 Multiply.




Now that the fractions have equal denominators, we can combine them:


%2810z%2B5-%283z-18%29%29%2F%2815z%29 Combine the fractions.


%2810z%2B5-3z%2B18%29%2F%2815z%29 Distribute


%287z%2B23%29%2F%2815z%29 Combine like terms.



So %282z%2B1%29%2F%283z%29-%28z-6%29%2F%285z%29 simplifies to %287z%2B23%29%2F%2815z%29



In other words, %282z%2B1%29%2F%283z%29-%28z-6%29%2F%285z%29=%287z%2B23%29%2F%2815z%29 where z%3C%3E0






# 2



Problem:

solve
1. 5b^2-15b=0


Solution:


5b%5E2-15b=0 Start with the given equation


5b%28b-3%29=0 Factor out the GCF 5b


Now set each factor equal to zero:


5b=0 or b-3=0


b=0 or b=3 Now solve for b in each case


So our answers are

b=0 or b=3