|0.1x-2.2|+0.2is greater than or equal to 0.7

Answer 1

| 0.1x - 2.2 | + 0.2 >= 0.7

| 0.1x - 2.2 | >= 0.7

0.1x - 2.2 > 0.7 or 0.1x - 2.2 <= -0.7

0.1x > 2.9 or 0.1x <= 1.5

x > 29 or x <=15

Answer 2

We'll start with regular algebra.

|0.1x - 2.2| + 0.2 ≥ 0.7

|0.1x - 2.2| ≥ 0.5

Now, remember that the "value" inside the absolute value symbols can be negative or positive. |8| = |-8| = 8, for example (absolute value is the distance from 0, and we normally measure distance with positive numbers).

The trick with inequalities, though, is that, in order to have an absolute value ≥ 0.5, the negative value has to be ≤ -0.5 because the closer we get to 0, the smaller the absolute value, but we want the absolute value to be ≥ 0.5. D'oh!

0.1x - 2.2 ≥ 0.5

0.1x ≥ 2.7

x ≥ 27

0.1x - 2.2 ≤ -0.5

0.1x ≤ 1.7

x ≤ 17

17 ≥ x ≥ 27

Let's check with a number that fits neither, like 20.

|0.1(20) - 2.2| + 0.2 ≥ 0.7

|2 - 2.2| + 0.2 ≥ 0.7

|-0.2| + 0.2 ≥ 0.7

0.2 + 0.2 ≥ 0.7

0.4 ≥ 0.7

0 ≥ 0.3

Hey, that's not true! You can also check with numbers that do fit, like -20 and 30 to make sure, but it looks like we are good.