Question

solve the equation $y + 5 = \frac{1}{2}y + 6$. what is the value of $y$? $y = \square$

Explanation:

Step1: Subtract $\frac{1}{2}y$ from both sides

To get all the \( y \)-terms on one side, we subtract \(\frac{1}{2}y\) from both sides of the equation \( y + 5=\frac{1}{2}y + 6 \). This gives us \( y-\frac{1}{2}y+5=\frac{1}{2}y-\frac{1}{2}y + 6 \), which simplifies to \(\frac{1}{2}y+5 = 6\).

Step2: Subtract 5 from both sides

Next, we want to isolate the term with \( y \). So we subtract 5 from both sides of the equation \(\frac{1}{2}y+5 = 6\). This results in \(\frac{1}{2}y+5 - 5=6 - 5\), which simplifies to \(\frac{1}{2}y = 1\).

Step3: Multiply both sides by 2

To solve for \( y \), we multiply both sides of the equation \(\frac{1}{2}y = 1\) by 2. So \(2\times\frac{1}{2}y=2\times1\), which gives us \( y = 2 \).

Answer:

\( y = 2 \)