Questions: For each value of y, determine whether it is a solution to -47>-9y+7. y Is it a solution? Yes No --------- 1 ○ 6 ○ 10 ○ ○ -6

Transcript text: For each value of $y$, determine whether it is a solution to $-47>-9 y+7$. \begin{tabular}{|c|c|c|} \hline \multirow{2}{*}{$y$} & \multicolumn{2}{|c|}{ Is it a solution? } \\ \cline { 2 - 3 } & Yes & No \\ \hline 1 & $\bigcirc$ & \\ \hline 6 & $\bigcirc$ & \\ \hline 10 & $\bigcirc$ & $\bigcirc$ \\ \hline-6 & & \\ \hline \end{tabular}

Solution

Solution Steps

To determine whether each value of $ y $ is a solution to the inequality $-47 > -9y + 7$, we will substitute each value of $ y $ into the inequality and check if the inequality holds true. If it does, then the value is a solution; otherwise, it is not.

Step 1: Substitute $ y = 1 $

For $ y = 1 $: \[ -9(1) + 7 = -9 + 7 = -2 \] Now check the inequality: \[ -47 > -2 \quad \text{(False)} \] Thus, $ y = 1 $ is not a solution.

Step 2: Substitute $ y = 6 $

For $ y = 6 $: \[ -9(6) + 7 = -54 + 7 = -47 \] Now check the inequality: \[ -47 > -47 \quad \text{(False)} \] Thus, $ y = 6 $ is not a solution.

Step 3: Substitute $ y = 10 $

For $ y = 10 $: \[ -9(10) + 7 = -90 + 7 = -83 \] Now check the inequality: \[ -47 > -83 \quad \text{(True)} \] Thus, $ y = 10 $ is a solution.

Step 4: Substitute $ y = -6 $

For $ y = -6 $: \[ -9(-6) + 7 = 54 + 7 = 61 \] Now check the inequality: \[ -47 > 61 \quad \text{(False)} \] Thus, $ y = -6 $ is not a solution.