Solve for X:|36 − 2x| < 204

Answer 1

|36 − 2x| < 204

If 36-2x > 0 then 36 -2x < 204

If 36 – 2x < 0 then 36 – 2x > -204

This equation is solved for all x where

-204 < 36 – 2x < 204

Remember to flip the sense of the inequality when dividing or multiplying by a negative value

36 -2x > -204                    36 – 2x < 204

-2x > -240                               -2x < 168

X < -240/-2                                x > 168/-2

X < 120                                      x > -84

Answer 2

|36 - 2x| < 204

You need to consider 2 cases: 36 - 2x is positive, and 36 - 2x is negative

Positive case:

|36 - 2x| positive ⇒ |36 - 2x| = 36 - 2x

36 - 2x < 204 ⇒

x > (36 - 204)/2

x > -84

Negative case:

|36 - 2x| negative ⇒ |36 - 2x| = -(36 - 2x) = 2x - 36

2x - 36 < 204

x < (204 + 36)/2

x < 120

Combine the results of the positive and negative cases and get

-84 < x < 120

Test the answer.

Answer 3

Set up two inequalities.

36 - 2x < 204 AND 36 - 2x > - 204

- 2x < 168. - 2x > - 240

Recall that when dividing both sides of an inequality, the direction of the inequality sign reverses.

x > 84. AND x < - 240

Regards,

Anita A.

Answer 4

Inequality expressions can be tricky, but not impossible. The first thing we have here is;

| 36 - 2x | < 204

When it comes to an absolute value in an inequality, we need to simplify the expression. Take the following for example:

|22 + x| < 50. We can observe this through the following theory; |ax + b| < c , where c > 0.

Another thing to note is where the values of x rest on a number line for this inequality. We do this by setting up the inequality such that the output of |22 + x| provides us with a number no greater than 50, but greater than -50;

-50 < 22 + x < 50

Now we can solve the inequality. It looks a bit tricky, but you can split up this inequality into 2 separate problems:

1. -50 < 22 + x
2. 22 + x < 50

From here, a little algebra can solve out the inequalities, and thus provide an answer for x . You should be able to apply this theory to your question, and run it through to solve it.

Hope this helps! :)