Absolute Value

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

For this problem, that gives us a final answer of 10.

Here, we have to split the problem up into two parts:

and

Let's start with the first equation:

First, we can add to each side:

Now we divide by -6. Remember, when you divide by a negative, you flip the sign of the inequality:

Which we can reduce:

Now let's do the other part of the problem the same way:

To solve an absolute value inequality, first isolate the absolute value expression, which can be done here by subtracting 35 from both sides:

There is no need to go further. The absolute value of any number is always greater than or equal to 0, so, regardless of the value of ,

.

Therefore, the solution set is the set of all real numbers.

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

For this problem, that gives us a final answer of 25.

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

For this problem, that gives us a final answer of 12.

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

For this problem, that gives us a final answer of 7.

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

For this problem, that gives us a final answer of 129.

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

For this problem, that gives us a final answer of 14.

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

For this problem, that gives us a final answer of 10.