Question

for each value of y, determine whether it is a solution to 7 + 5y > 42.

is it a solution?	yes	no
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Explanation:

First, we solve the inequality \(7 + 5y>42\) for \(y\).

Step 1: Subtract 7 from both sides

Subtract 7 from each side of the inequality to isolate the term with \(y\).
\(7 + 5y-7>42 - 7\)
Simplifying both sides, we get \(5y>35\).

Step 2: Divide by 5

Divide both sides of the inequality by 5 to solve for \(y\).
\(\frac{5y}{5}>\frac{35}{5}\)
Simplifying, we find \(y > 7\).

Now we check each value of \(y\):

For \(y=- 3\):

We check if \(-3>7\). Since \(-3\) is less than 7, \(-3\) is not a solution.

For \(y = 0\):

We check if \(0>7\). Since \(0\) is less than 7, \(0\) is not a solution.

For \(y=9\):

We check if \(9>7\). Since \(9\) is greater than 7, \(9\) is a solution.

For \(y = 7\):

We check if \(7>7\). Since \(7\) is not greater than 7 (it is equal), \(7\) is not a solution.

Answer:

• For \(y=-3\): No
• For \(y = 0\): No
• For \(y=9\): Yes
• For \(y = 7\): No

So in the table:

• For \(y=-3\), mark "No"
• For \(y = 0\), mark "No"
• For \(y=9\), mark "Yes"
• For \(y = 7\), mark "No"