Question

How do you solve `2y+6<2(y+7)`?

Answer 1

See a solution process below:

Explanation:

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

`2y + 6 < color(red)(2)(y + 7)`

`2y + 6 < (color(red)(2) * y) + (color(red)(2) * 7)`

`2y + 6 < 2y + 14`

Next, subtract `color(red)(2y)` from each side of the inequality:

`-color(red)(2y) + 2y + 6 < -color(red)(2y) + 2y + 14`

`0 + 6 < 0 + 14`

`6 < 14`

Because 6 is in fact less than 14 the solution to this inequality is `y` can be any number and this inequality will be true. Therefore the solution is `y = {RR}`