Question

Question #b1d22

Answer 1

Find the number that makes the statement true
`b=16`

Explanation:

As there is no formatting, the question is a bit ambiguous.

If it is to be read as `4/(b+2) =2/9`, then we have:

`b` is the missing number, and `4/2` does not equal `2/9`.

`2/9 = 0.222...`

Compare both fractions,

`4/b+2 and 2/9.`

After comparing both fractions I saw that

`2xx2 = 4`

`9xx2 = 18`

`16+2 = 18`

so `b` must equal `16.`

`4/(16+2) = 4/18 = 2/9`

Answer 2

`b=-9/4`

Explanation:

We have to solve the equation for b so we need to isolate it so that b equals something. Starting with:

`4/b+2=2/9`

fist we subtract 2 from both sides:

`4/b=2/9-2`

now we convert that two into a fraction with 9 as the denominator:

`4/b=2/9-18/9`

subtract the fractions from each other:

`4/b=-16/9`

multiply both sides by `b`:

`4=-16/9b`

multiply both sides by 9:

`4*9=-16b`

divide both sides by 16:

`(4*9)/16=-b`

divide top and bottom of the left side by 4:

`9/4=-b`

and finally we multiply both sides by -1 so we can get a positive `b`:

`b=-9/4`

Answer 3

`b = -9/4`

Explanation:

In an equation with fractions, you can get rid of the denominators immediately by multiplying each fraction by the LCD.

`color(white)(xxxxxxx)4/b +2 = 2/9" "larr LCD = color(blue)(9b)`

`(color(blue)(9cancelbxx)4)/cancelb + color(blue)(9bxx)2 = (color(blue)(cancel9bxx)2)/cancel9`

This leaves us with an equation without fractions:

`36+18b = 2b`

`36 = 2b-18b`

`36 = -16b`

`36/-16 =b`

`b = -9/4`