Solving an Absolute Value Equation

Solve $1 = 4 | x - 2 | + 2.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Isolating the absolute value on one side of the equation gives the following.

$\begin{array}{l} 1 = 4 | x - 2 | + 2 \\ - 1 = 4 | x - 2 | \\ - \frac{1}{4} = | x - 2 | \end{array}$
The absolute value always returns a positive value, so it is impossible for the absolute value to equal a negative value. At this point, we notice that this equation has no solutions.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find where the graph of the function $f (x) = - | x + 2 | + 3$ intersects the horizontal and vertical axes.

How did it go?