Question

Use properties and definitions of operations to show that the statement is true. Justify each step?

(12b + 15) - 1b = 15b +9b

Answer 1

There are many ways to answer this depending on how thorough your instructor was and what level you are at. This seems somewhat exhaustive... delete what you don't need.
associative property of addition 12b+15-1b=15b+9b
commutative property of addition 12b-1b+15=15b+9b
combining like terms 11b+15=24b
additive inverse and balancing equations 11b-11b+15=24b-11b
simplify by subtracting like terms 15=13b
multiplicative inverse and balancing equations 15/13=13b/13
simplify through division b=15/13
now check by substitution ( I leave that to you)

Answer 2

Thats exactly what I needed thanks!(:

Answer 3

cool

Answer 4

That wasn't correct

Answer 5

(12b + 15) - 1b = 15b +9b ... Starting statement


(15 + 12b) - 1b = 15b +9b ... Commutative property of addition


15 + (12b - 1b) = 15b +9b ... Associative property of addition


15 + ( (12 - 1)b ) = (15 + 9)b ... Distributive property


15 + 11b = 24b ... Arithmetic (12-1 = 11 and 15+9 = 24)


Do you see how I'm getting all this and where I'm going with it? If not let me know.


After that last step, what's next?

Answer 6

Uh I think so..would you subtract 11b from both sides, getting 13b, then divide from both sides?

Answer 7

divide both sides by what

Answer 8

and b would equal 15/13?

Answer 9

you are correct

Answer 10

by 13?

Answer 11

Okay thank you so much!!(:

Answer 12

yes, the answer is \[\Large b = \frac{15}{13}\]

Answer 13

You are amazing!(:

Answer 14

Here's the full detailed and step by step look at what's going on. You don't need to show all these steps, but hopefully they explain what's going on.


(12b + 15) - 1b = 15b +9b ... Starting statement


(15 + 12b) - 1b = 15b +9b ... Commutative property of addition


15 + (12b - 1b) = 15b +9b ... Associative property of addition


15 + ( (12 - 1)b ) = (15 + 9)b ... Distributive property


15 + 11b = 24b ... Arithmetic (12-1 = 11 and 15+9 = 24)


15 + 11b + (-11b) = 24b + (-11b) ... Addition property of equality


15 + 11b - 11b = 24b - 11b ... Rewrite +- as just -


15 + (11 - 11)b = (24 - 11)b ... Distributive property


15 + 0b = 13b ... Arithmetic (11-11 = 0 and 24-11 = 13)


15 = 13b ... Simplification


15/13 = 13b/13 ... Division property of equality


15/13 = 1b ... Arithmetic (13/13 = 1)


15/13 = b ... Simplification


b = 15/13 ... Flip the equation

This is just extra. You probably don't need it though, but it doesn't hurt to have a look.