Questions: Solve x=8 x= Solve. Separate your answers with a comma. x-4=4 Solve the equation 5x-1=19 The solutions are:

Transcript text: Solve $|x|=8$ $x=$ $\square$ To give multiple answers, list your answers separated by a comma Solve. Separate your answers with a comma. \[ |x-4|=4 \] $\square$ Solve the equation $|5 x-1|=19$ The solutions are: $\square$

Solution

Solution Steps

Step 1: Solve $|x| = 8$

The absolute value equation $|x| = 8$ implies that $x$ can be either $8$ or $-8$.
Thus, the solutions are:
$x = 8, -8$

Step 2: Solve $|x - 4| = 4$

The absolute value equation $|x - 4| = 4$ implies two cases:

$x - 4 = 4$, which gives $x = 8$.
$x - 4 = -4$, which gives $x = 0$.
Thus, the solutions are:
$x = 8, 0$

Step 3: Solve $|5x - 1| = 19$

The absolute value equation $|5x - 1| = 19$ implies two cases:

$5x - 1 = 19$, which gives $5x = 20$ and $x = 4$.
$5x - 1 = -19$, which gives $5x = -18$ and $x = -\frac{18}{5}$.
Thus, the solutions are:
$x = 4, -\frac{18}{5}$