# Absolute value equation with no solution | Linear equations | Algebra I | Khan Academy | Summary and Q&A

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August 14, 2013
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Absolute value equation with no solution | Linear equations | Algebra I | Khan Academy

## TL;DR

The equation with absolute values is simplified to find that there is no solution for x.

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### Q: How can the equation 4|𝑥+10|+4 = 6|𝑥+10|+10 be simplified?

The equation can be simplified by subtracting 6|𝑥+10| from both sides, resulting in -2|𝑥+10| = 6.

### Q: Why is there no solution for |𝑥+10|= -3?

The absolute value of any expression is always non-negative, so there is no value of 𝑥 that will make |𝑥+10| equal to a negative number. Therefore, there is no solution.

### Q: Can the equation be solved in a different way to find a solution for 𝑥?

No, because the basic properties of absolute value dictate that it will always yield a non-negative value. In this specific equation, there is no way to obtain a negative value, so a solution for 𝑥 cannot be found.

### Q: How would the solution change if the equation was 4|𝑥+10|+4 = 6|𝑥+10|+12?

The equation would still have no solution because the extra constant term (+12) does not affect the fundamental nature of the equation, which relies on the properties of absolute value.

## Summary & Key Takeaways

• The equation 4|𝑥+10|+4 = 6|𝑥+10|+10 is given and the goal is to solve for 𝑥.

• By isolating the absolute value expression on one side, the equation becomes -2|𝑥+10| = 6.

• Dividing both sides by -2 leads to |𝑥+10| = -3, which results in the realization that there is no solution for 𝑥.