Question #b1d22

3 Answers

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#

Aug 11, 2017

#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#

Aug 11, 2017

#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#