# How do you solve |10x + 2| - 18 = -12?

Mar 7, 2016

This is an absolute value equation. As a result, we must consider two scenarios: that the absolute value is positive or negative.

#### Explanation:

First, before I solve the equation, let me prove the point I made above to further your understanding.

Let's look at an extremely simple equation involving absolute value.

$| x | = 2$

An absolute value, by definition, means the distance on the number line between 0 and the number. This distance doesn't take into account direction and therefore always is positive.

So, we must consider in the above equation the following:

x = 2 or -x = 2

x = 2 or x = -2

Checking these solutions back in the equation, you'll notice both will work, since $| - 2 | = 2$

We must first isolate the absolute value:

$| 10 x + 2 | = 6$

$10 x + 2 = 6 \mathmr{and} - \left(10 x + 2\right) = 6$

$10 x = 4 \mathmr{and} - 10 x - 2 = 6$

$x = \frac{2}{5} \mathmr{and} - \frac{4}{5}$

Hopefully this helps, and happy voting tomorrow!
The text passage contains a mathematical question involving an absolute value equation and provides a detailed explanation and solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# How do you solve |10x + 2| - 18 = -12?

Mar 7, 2016

This is an absolute value equation. As a result, we must consider two scenarios: that the absolute value is positive or negative.

#### Explanation:

First, before I solve the equation, let me prove the point I made above to further your understanding.

Let's look at an extremely simple equation involving absolute value.

$| x | = 2$

An absolute value, by definition, means the distance on the number line between 0 and the number. This distance doesn't take into account direction and therefore always is positive.

So, we must consider in the above equation the following:

x = 2 or -x = 2

x = 2 or x = -2

Checking these solutions back in the equation, you'll notice both will work, since $| - 2 | = 2$

We must first isolate the absolute value:

$| 10 x + 2 | = 6$

$10 x + 2 = 6 \mathmr{and} - \left(10 x + 2\right) = 6$

$10 x = 4 \mathmr{and} - 10 x - 2 = 6$

$x = \frac{2}{5} \mathmr{and} - \frac{4}{5}$

Hopefully this helps, and happy voting tomorrow!
user
The text passage contains a mathematical question involving an absolute value equation and provides a detailed explanation and solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER