SOLUTION: Please show me how to check this problem: 2 + 11b = 8b + 15 b=4 1/3 I am having trouble checking this problem with the fractions can you show me how to do it.

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Question 1047258: Please show me how to check this problem:
2 + 11b = 8b + 15
b=4 1/3
I am having trouble checking this problem with the fractions can you show me how to do it.
Found 4 solutions by solver91311, ewatrrr, Theo, MathLover1:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!

Change the mixed number to an improper fraction. Substitute the improper fraction for the variable in the original equation. Then multiply both sides of the equation by the denominator of the improper fraction. The rest is just straight up integer arithmetic.

John

My calculator said it, I believe it, that settles it

Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
2 + 11b = 8b + 15
3b = 15 - 2
b = 13/3
b=4 1/3 = 13/3
2 + 11(13/3) =? 8(13/3) + 15
6 + 11*13 =? 8*13 + 45
6 + 143 = 104 + 45
149 = 149 CHECKS

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
start with 2 + 11 * b = 8 * b + 15
subtract 8 * b from both sides of the equation and subtract 2 from both sides of the equation to get 11 * b - 8 * b = 15 - 2
combine like terms to get 3 * b = 13
divide both sides of the equation by 3 to get b = 13 / 3
this is equivalent to 4 and 1/3.

to confirm that the solution is correct, do the following.
replace b with (4 + 1/3).
your equation of 2 + 11 * b = 8 * b + 15 becomes:
2 + 11 * (4 + 1/3) = 8 * (4 + 1/3) + 15

simplify to get:

2 + 11 * 4 + 11 * 1/3 = 8 * 4 + 8 * 1/3 + 15

simplify by performing the arithmetic to get:

2 + 44 + 11/3 = 32 + 8/3 + 15

combine the whole numbers to get:

46 + 11/3 = 47 + 8/3

since 11/3 is equal to 3 + 2/3 and since 8/3 is equal to 2 + 2/3, your equation becomes:

46 + 3 + 2/3 = 47 + 2 + 2/3

add the whole numbers together to get:

49 + 2/3 = 49 + 2/3

since the equation is true, your solution is correct.

another way to do it is to work with improper fractions and make make everything under the same common denominator.

you have b = 4 and 1/3.
convert this to an improper fraction that is equal to 13/3.

replace b with 13/3 in the original equation.
you get 2 + 11 * 13/3) = 8 * 13/3 + 15

simplify to get:

2 + 143/3 = 104/3 + 15

multiply both sides of the equation by 3 to get 6 + 143 = 104 + 45

combine like terms to get 149 = 149

since the left side of the equation is equal to the right side of the equation, the equation is true and your solution is confirmed to be good.

another way is to convert the answer to decimal form and store it in your calculator and then use the stored value in place of b.

4 and 1/3 is equal to 4.333333.......

store the result the calculator gave you in memory.

now take your original equation of 2 + 11 * b = 8 * b + 15 and used the stored value in place of b.

you will get 2 + 11 * 4.33333..... = 8 * 4.333333..... + 15.

calculate the left side of the equation in your calculator to get 49.666666.....

calculate the right side of the equation in your calculator to get 49.6666666.....

they're the same so the solution is good.

the general procedure is to replace the variables in your original equation with the values you calculated for them to see if the original equation is true.

the original equation is true if the value on the left side of the equal sign is the same as the value on the right side of the equal sign.

if the original equaiton is true, then the solution can be assumed to be good.

Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!

=
to check this problem start with given equation
substitute for , will be easier to use fraction then mix number

-> left and right sides are equal which confirms our solution is correct