Question

How do you solve `-5(m-1)+3(2m-1)=8` using the distributive property?

Answer 1

See the entire solution process below:

Explanation:

First, expand both terms in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(-5)(m - 1) + color(blue)(3)(2m - 1) = 8`

`(color(red)(-5) * m) + (color(red)(-5) * -1) + (color(blue)(3) * 2m) - (color(blue)(3) * 1) = 8`

`-5m + 5 + 6m - 3 = 8`

Next, group and combine like terms on the left side of the equation:

`6m - 5m + 5 - 3 = 8`

`(6 - 5)m + (5 - 3) = 8`

`1m + 2 = 8`

`m + 2 = 8`

Now, subtract `color(red)(2)` from each side of the equation to solve for `m` while keeping the equation balanced:

`m + 2 - color(red)(2) = 8 - color(red)(2)`

`m + 0 = 6`

`m = 6`