Answer
$x=4$ and $x=-\dfrac{3}{2}$ satisfy the given conditions
Work Step by Step
$y=|5-4x|$ and $y=11$
Substitute $y$ by $11$:
$|5-4x|=11$
Solving an absolute value equation is equivalent to solving two separate equations, which are $5-4x=11$ and $5-4x=-11$.
Solve these two equations for $x$:
$5-4x=11$
$-4x=11-5$
$-4x=6$
$x=-\dfrac{6}{4}$
$x=-\dfrac{3}{2}$
$5-4x=-11$
$-4x=-11-5$
$-4x=-16$
$x=\dfrac{-16}{-4}$
$x=4$
$x=4$ and $x=-\dfrac{3}{2}$ satisfy the given conditions