Answer
The solution is $y = 10$ or $y = -6$.
Work Step by Step
To solve absolute value equations, we get rid of the absolute value sign by setting the expression within the absolute value sign equal to the constant given, but with opposite signs. For this problem, we set up the problem this way:
$2y - 4 = 16$ or $2y - 4 = -16$
Solve each equation.
First equation:
$2y - 4 = 16$
$2y = 4 + 16$
$2y = 20$
Divide both sides of the equation by $2$ to solve for $y$:
$y = 10$
Second equation:
$2y - 4 = -16$
$2y = 4 - 16$
$2y = -12$
Divide both sides of the equation by $2$ to solve for $y$:
$y = -6$
The solutions are $y = 10$ and $y = -6$.
Check our answers by plugging them into the original equation to see if it holds true.
For $y = 10$:
$|2(10) - 4| = 16$
$|20 - 4| = 16$
$|16| = 16$
$16 = 16$
For $y = -6$:
$|2(-6) - 4| = 16$
$|-12 - 4| = 16$
$|-16| = 16$
$16 = 16$
The two sides equal one another; therefore; $y = -6$ is also a valid solution.
