Question

How do you solve `1/2(4x-6)=11` using the distributive property?

Answer 1

See a solution process below:

Explanation:

First, expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(1/2)(4x - 6) = 11`

`(color(red)(1/2) xx 4x) - (color(red)(1/2) xx 6) = 11`

`4/2x - 6/2 = 11`

`2x - 3 = 11`

Next, add `color(red)(3)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`2x - 3 + color(red)(3) = 11 + color(red)(3)`

`2x - 0 = 14`

`2x = 14`

Now, divide each side of the equation by `color(red)(2)` to solve for `x` while keeping the equation balanced:

`(2x)/color(red)(2) = 14/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 7`

`x = 7`