Problem

Solve the absolute value equation or indicate that the equation has no solution.
\[
|6 x-3|+4=4
\]

Answer

Expert–verified
Hide Steps
Answer

Final Answer: The solution to the equation is \(\boxed{\frac{1}{2}}\).

Steps

Step 1 :The absolute value equation is \(|6x - 3| + 4 = 4\).

Step 2 :To solve this equation, we first isolate the absolute value term. This gives us \(|6x - 3| = 4 - 4 = 0\).

Step 3 :The absolute value of a number is always non-negative, so the only way for \(|6x - 3|\) to equal 0 is if \(6x - 3 = 0\).

Step 4 :We can solve this equation for x to find the solution to the original absolute value equation.

Step 5 :The solution to the equation is \(x = \frac{1}{2}\). This is the only value of x that makes the absolute value equation true.

Step 6 :Final Answer: The solution to the equation is \(\boxed{\frac{1}{2}}\).

link_gpt