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

TL;DR

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

Key Insights

• 😑 The equation with absolute values can be simplified by isolating the absolute value expression on one side.
• 🗂️ Dividing an absolute value equation by a negative number reverses the inequality.
• 🚱 The non-negativity property of absolute value should be considered when solving equations involving absolute values.

Transcript

So we're asked to solve for x, and we have this equation with absolute values in it. So it's 4 times the absolute value of x plus 10 plus 4 is equal to 6 times the absolute value of x plus 10 plus 10. And at first, this looks really daunting, but the key is to just solve for this absolute value expression and then go from there. Let me just rewrite... Read More

Questions & Answers

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.