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.
Questions & Answers
Q: How can the equation 4𝑥+10+4 = 6𝑥+10+10 be simplified?
The equation can be simplified by subtracting 6𝑥+10 from both sides, resulting in 2𝑥+10 = 6.
Q: Why is there no solution for 𝑥+10= 3?
The absolute value of any expression is always nonnegative, 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 nonnegative 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 4𝑥+10+4 = 6𝑥+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 4𝑥+10+4 = 6𝑥+10+10 is given and the goal is to solve for 𝑥.

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

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