Question

How do you solve and write the following in interval notation: `2x - 3<5` or `3x - 2 >13`?

Answer 1

See a solution process below:

Explanation:

Inequality 1:
Start to solve this inequality by adding `color(red)(3)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`2x - 3 + color(red)(3) < 5 + color(red)(3)`

`2x - 0 < 8`

`2x < 8`

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

`(2x)/color(red)(2) < 8/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 4`

`x < 4`

Inequality 2
Start to solve this inequality by adding `color(red)(2)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`3x - 2 + color(red)(2) > 13 + color(red)(2)`

`3x - 0 > 15`

`3x > 15`

Now, divide each side of the inequality by `color(red)(3)` to solve for `x` while keeping the inequality balanced:

`(3x)/color(red)(3) > 15/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) > 5`

`x > 5`

**The solution is: `x < 4` and `x > 5`

Or, in interval notation:

`(-oo, 4)` and `(5, +oo)`