Question

How do you solve `4y + 7- y > 3( y + 3)`?

Answer 1

See a solution process below:

Explanation:

First, group and combine like terms on the left side of the inequality:

`4y - y + 7 > 3(y + 3)`

`4y - 1y + 7 > 3(y + 3)`

`(4 - 1)y + 7 > 3(y + 3)`

`3y + 7 > 3(y + 3)`

Next, expand the term in parenthesis on the right side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:

`3y + 7 > (3 * y) + (3 * 3)`

`3y + 7 > 3y + 9`

Now, subtract `color(red)(3y)` from each side of the inequality:

`3y - color(red)(3y) + 7 > 3y - color(red)(3y) + 9`

`0 + 7 > 0 + 9`

`7 > 9`

We know `7` is not greater than `9` therefore there are no values of `y` which make this inequality true.

Therefore, the solution is the null or empty set: `y = {O/}`