To solve the equation:

$\frac{|x - 4|}{2} + 10 = 7$

Step 1: Isolate the absolute value expression

First, subtract 10 from both sides of the equation to isolate the absolute value term:

$\frac{|x - 4|}{2} = 7 - 10$ $\frac{|x - 4|}{2} = -3$

Step 2: Check for a valid solution

Since the absolute value function, $|x - 4|$, always gives a non-negative result (greater than or equal to 0), it is impossible for $\frac{|x - 4|}{2}$ to equal $-3$. Therefore, there is no solution for this equation.

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Related Questions:

1. How do you solve absolute value equations in general?
2. What happens if the right-hand side of an equation is negative in absolute value equations?
3. Can an absolute value equation have multiple solutions?
4. How do you solve absolute value inequalities?
5. What are the properties of absolute value functions?

Tip:

When solving absolute value equations, always check if the equation leads to a possible solution since the absolute value cannot produce a negative result.