How do you solve \frac { 1} { 2} b - 9= 4b + 5?

2 Answers
Jan 6, 2018

b=-4

Explanation:

To solve this equation, you need to isolate all of the terms with b on one side (usually the left) and isolate all of the terms without b on the other (usually the right):

1/2b-9 = 4b+5

Adding 9 to both sides:

1/2b-9+9=4b+5+9
1/2b=4b+14

To make things easier for us later, we can multiply both sides by 2 to get rid of the 1/2:

2(1/2b)=2(4b+14)
b=2(4b)+2(14)
b=8b+28

Subtracting 8b from both sides:

b-8b=8b-8b+28
-7b=28

Dividing both sides by -7:

{-7b}/{-7}=28/{-7}
b=-4

To check our work, we can plug in -4 for b and test the equality:

1/2(-4)-9 = 4(-4)+5
-2-9=-16+5
-11=-11

Since this equality works out, we did everything right.

Jan 6, 2018

See explanation

Explanation:

1/2b = 4b + 14 rarr Add 9 to each side

b = 8b + 28 rarr Multiply each side by 2 to get rid of the fraction

-7b = 28 rarr Subtract 8b from each side

b = -4 rarr Divide each side by -7