Solve the following linear inequalities using the addition and subtraction properties of equality.
$5\le y+3$

• A. $2>y$
• B. $8\le y$
• C. $2\le y$
• D. $2\ge y$

Answer: (C)

Verified step by step guidance

1. Start with the first inequality: \$5 \le y + 3\(. To isolate \)y\(, use the subtraction property of inequality by subtracting 3 from both sides: \)5 - 3 \le y + 3 - 3$.
2. Simplify both sides: \$2 \le y\(. This means \)y$ is greater than or equal to 2.
3. Next, look at the second inequality: \$2 > y\(. This can be rewritten as \)y < 2\( to express \)y$ on the left side.
4. The third inequality is \$8 \le y\(, which means \)y$ is greater than or equal to 8.
5. Now, analyze all inequalities together to find the values of \(y\) that satisfy all conditions. Compare the ranges from each inequality to determine the solution set.