How do you solve \frac { 8} { 3} = \frac { m - 5} { m - 10}83=m5m10?

2 Answers
Aug 1, 2017

m=13m=13

Explanation:

8/3=(m-5)/(m-10)83=m5m10

Multiply both sides by 3(m-10)3(m10).

3(m-10)xx8/3=3(m-10)xx(m-5)/(m-10)3(m10)×83=3(m10)×m5m10

cancel3(m-10)xx8/cancel3=3cancel((m-10))xx(m-5)/cancel(m-10)

(m-10)xx8=3xx(m-5)

Open the brackets and simplify.

8m-80=3m-15

Subtract 3m from each side.

8m-3m-80=3m-3m-15

5m-80=-15

Add 80 to each side.

5m+80-80=80-15

5m=65

Divide both sides by 5.

(5m)/5=65/5

(cancel5m)/cancel5=(13cancel65)/(1cancel5)

m=13

Aug 1, 2017

m=13

Refer to the explanation for the process.

Explanation:

Solve:

8/3=(m-5)/(m-10)

Cross multiply. Multiply the denominators by the numerators of the opposite fractions.

(8(m-10))/(3(m-5))

Expand.

8m-80=3m-15

Subtract 3m from both sides.

8m-80-3m=3m-3m-15

Cancel 3m on the right side.

8m-80-3m=color(red)cancel(color(black)(3m))-color(red)cancel(color(black)(3m))-15

Simplify.

5m-80=-15

Add 80 to both sides.

5m-80+80=-15+80

Cancel 80 on the left side.

5m-color(red)cancel(color(black)(80))+color(red)cancel(color(black)(80))=-15+80

Simplify.

5m=65

Divide both sides by 5.

(5m)/5=65/5

Cancel 5 on the left side.

(color(red)cancel(color(black)(5^1))m)/color(red)cancel(color(black)(5^1))=65/5

Simplify.

m=13