In this example, we need to subtract 3 from both sides; then divide both sides by `-2` (remembering to change the direction of the inequality).

`3-2x>=15`

`-2x>=15-3`

`-2x>=12`

`x<=12/(-2)`

`x<=-6`

Here's the graph of this solution:

10-1-2-3-4-5-6-7-8xOpen image in a new page

(Note the change in sense due to dividing by a negative number)

Check: Always check your solution and you can be sure your answer is correct.

In this case, any number less than `-6` should "work" in the original equation, and any number bigger than `-6` should fail.

Let's take `x = -10` (a convenient number less than `-6`)

LHS `= 3 − 2(-10) = 3 + 20 = 23`. This is more than `15` so it is true.

Now let's take `x = 0` (a convenient number greater than `-6`)

LHS `= 3 − 2(0) = 3`. This is NOT more than `15`, which is what we hoped for.

So we can be sure our answer is correct.