Question

How do you solve and write the following in interval notation: `-4x< -16` and `x+ 4 > 5`?

Answer 1

See a solution process below:

Explanation:

Solution To Inequality 1

`-4x < -16`

We will divide each side of the inequality by `color(blue)(-4)` to solve for `x` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`(-4x)/color(blue)(-4) color(red)(>) (-16)/color(blue)(-4)`

`(color(blue)(cancel(color(black)(-4)))x)/cancel(color(blue)(-4)) color(red)(>) 4`

`x > 4`

Solution To Inequality 2

`x + 4 > 5`

We will subtract `color(red)(4)` from each side of the equation to solve for `x` while keeping the equation balanced:

`x + 4 - color(red)(4) > 5 - color(red)(4)`

`x + 0 > 1`

`x > 1`

The Solutions Are: `x > 1` and `x > 4`

However, because the interval `(1, 4)` is a valid solution for Inequality 2 but not for inequality 1 the solution is:

`x > 4`

Interval notation:

`(4, +oo)`