Question

for each value of y, determine whether it is a solution to \\(\frac{y}{5} - 8 = -12\\). table with columns: y, is it a solution? (yes, no); rows: 50, -20, 30, 0 (each with empty circles for yes/no). two buttons (refresh, ×) are interface elements.

Explanation:

To determine if a value of \( y \) is a solution to the equation \( \frac{y}{5}-8 = -12 \), we substitute each \( y \) value into the equation and check if the equation holds true.

Step 1: Solve the equation for \( y \) (optional, but helpful)

Start with the equation:
\[
\frac{y}{5}-8=-12
\]
Add 8 to both sides:
\[
\frac{y}{5}=-12 + 8
\]
\[
\frac{y}{5}=-4
\]
Multiply both sides by 5:
\[
y=-4\times5
\]
\[
y = - 20
\]
So the solution to the equation is \( y=-20 \). Now we can check each given \( y \) value.

Step 2: Check \( y = 50 \)

Substitute \( y = 50 \) into \( \frac{y}{5}-8 \):
\[
\frac{50}{5}-8=10 - 8=2
\]
Since \( 2
eq - 12 \), \( y = 50 \) is not a solution.

Step 3: Check \( y=-20 \)

Substitute \( y=-20 \) into \( \frac{y}{5}-8 \):
\[
\frac{-20}{5}-8=-4-8=-12
\]
Since \( - 12=-12 \), \( y=-20 \) is a solution.

Step 4: Check \( y = 30 \)

Substitute \( y = 30 \) into \( \frac{y}{5}-8 \):
\[
\frac{30}{5}-8=6 - 8=-2
\]
Since \( -2
eq - 12 \), \( y = 30 \) is not a solution.

Step 5: Check \( y = 0 \)

Substitute \( y = 0 \) into \( \frac{y}{5}-8 \):
\[
\frac{0}{5}-8=0 - 8=-8
\]
Since \( -8
eq - 12 \), \( y = 0 \) is not a solution.

Answer:

• For \( y = 50 \): No
• For \( y=-20 \): Yes
• For \( y = 30 \): No
• For \( y = 0 \): No