Question

How do you solve `\frac { 5- b } { 3} = \frac { 2b + 2} { - 4}`?

Answer 1

First, let's clear the denominators:

`-4 xx (5-b) = (2b+2) xx 3`

`-20 + 4b = 6b + 6`

`4b = 6b = 26`

`-2b = 26`

`b =-13`

Let's check our work:

`(5+13)/3 = 6`

`(2 xx -13 + 2)/(-4) = 6`

Yep! `b = -13`

Answer 2

`b=-13`

Explanation:

There is ONE fraction on each side of the equal sign, so you may cross-multiply.

`color(blue)((5-b))/color(red)(3) = color(red)((2b+2))/color(blue)(-4)`

`color(red)(6b +6)=color(blue)(-20+4b)`

`6b-4b=-20-6`

`2b = -26`

`b =-13`

Answer 3

multiply both sides by each fraction's denominator, then solve for `b`, which would give you `b=-13`

Explanation:

What we will do is multiply both sides by the denominator of each side, thereby eliminating the need for fractions.

Starting with the left hand side:

`(5-b)/cancel(3)cancel(color(red)(xx3))=(2b+2)/(-4)color(red)(xx3)`

`5-b=((2b+2)color(red)(xx3))/(-4)`

`5-b=(6b+6)/(-4)`

Now, we multiply both sides by the denominator of the right-hand side:

`(5-b)color(red)(xx-4)=(6b+6)/cancel(-4)cancel(color(red)(xx-4))`

`-20+4b=6b+6`

Now, we'll re-arrange the equation so all of the terms related to `b` are on one side, and the constants are on the other:

`-20+cancel(4b)color(red)(-cancel(4b))=6b+6color(red)(-4b)`

`-20=2b+6`

`-20color(red)(-6)=2b+cancel(6)color(red)(-cancel(6))`

`-26=2b`

Finally, divide both sides by the constant `b` is multiplied by:

`-26/color(red)(2)=(cancel(2)b)/cancel(color(red)(2))`

`color(green)(b=-13)`