Question

Solve. Remember to check for extraneous solutions. Use a comma to separateanswers14 – 2y + 5 = 9Please explain!!

Answer 1

The solutions are:

`y=4`

and

`y=0`

Step-by-step explanation:

Given the equation:

`|4-2y|+5=9`

To solve for y:

Subract 5 from both sides

`\begin{gathered} |4-2y|+5-5=9-5 \\ |4-2y|=4 \end{gathered}`

Next, the absolute value always has two solutions:

`4-2y=4`

and

`4-2y=-4`

We need to solve each of these equations.

1.

`\begin{gathered} 4-2y=4 \\ \text{Subtract 4 from both sides} \\ 4-2y-4=4-4 \\ -2y=0 \\ y=(0)/(-2)=0 \end{gathered}`

2.

`\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=(-8)/(-2)=4 \end{gathered}`