Answer:
The solutions are:
[tex]y=4[/tex]
and
[tex]y=0[/tex]
Explanation:
Given the equation:
[tex]|4-2y|+5=9[/tex]
To solve for y:
Subract 5 from both sides
[tex]\begin{gathered} |4-2y|+5-5=9-5 \\ |4-2y|=4 \end{gathered}[/tex]
Next, the absolute value always has two solutions:
[tex]4-2y=4[/tex]
and
[tex]4-2y=-4[/tex]
We need to solve each of these equations.
1.
[tex]\begin{gathered} 4-2y=4 \\ \text{Subtract 4 from both sides} \\ 4-2y-4=4-4 \\ -2y=0 \\ y=\frac{0}{-2}=0 \end{gathered}[/tex]
2.
[tex]\begin{gathered} 4-2y=-4 \\ \text{Subtract 4 from both sides} \\ 4-2y-4=-4-4 \\ -2y=-8 \\ \text{Divide both sides by -2} \\ y=\frac{-8}{-2}=4 \end{gathered}[/tex]
