Question

How do you solve `(2x-9)/4<=x+2` and graph the solution on a number line?

Answer 1

`x ge -17/2`

Explanation:

Multiply both sides by `4`:

`(2x-9)/4 le x+2`

`4((2x-9)/4) le 4(x+2)`

`2x-9 le 4x+8`

Subtract `8` from both sides.

`2x-9-8 le 4x+8-8`

`2x - 17 le 4x`

Next, subtract `2x` from both sides.

`2x-17-2x le 4x - 2x`

`-17 le 2x`

Finally, divide both sides by 2.

`(-17)/2 le (2x)/2`

`-17/2 le x`

We can flip the inequality like this so it makes more sense:

`x ge -17/2`

Notice that the sign still points towards the bigger number (x). This inequality means that `x` is greater than `-17/2`, so to graph it on a number line, we will draw a solid dot on `-17/2` to indicate that `x` could be that number, and then shade in everything to the right of `-17/2`, since `x` can also be anything greater than it.

Final Answer