Question

How do you solve `2( x + 1) < - 3( x + 4) - 1`?

Answer 1

`x < -3`

Explanation:

Step 1) Expand the terms in parenthesis on each side of the inequality:

`2x + 2 < -3x - 12 - 1`

Step 2) Combine like terms on each side of the inequality:

`2x + 2 < -3x - 13`

Step 3) Solve for `x` while keeping each side of the inequality balanced:

`2x + 2 - 2 + 3x < -3x - 13 - 2 + 3x`

`5x < -15`

`(5x)/5 < -15/5`

`x < -3`

Answer 2

The solution of the inequality is `x < -3`.

Explanation:

First, simplify both sides of the inequality. On the left side, we need to distribute the `2`. On the right side, we need to distribute the `-3` and then combine like terms.

`2(x + 1) < -3(x + 4) - 1`
`2x + 2 < -3x - 12 - 1`
`2x + 2 < -3x - 13`

Now use inverse operations to get all the variable terms on the left side of the inequality and all the constant terms on the right side of the inequality. Then we will be able to solve the inequality.

`2x + 3x + 2 < -3x + 3x - 13`
`5x + 2 < -13`
`5x + 2 - 2 < -13 - 2`
`5x < -15`
`(5x)/5 < (-15)/5`
`x < -3`