For which of the inequalities below is $$ v \geq 4 $$ a solution? A. $$ v+5 \geq 9 $$ B. $$ v+59 $$ C. $$ v+5 \leq 8 $$ D. $$ v+5

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For which of the inequalities below is $$ v \geq 4 $$ a solution? A. $$ v+5 \geq 9 $$ B. $$ v+5>9 $$ C. $$ v+5 \leq 8 $$ D. $$ v+5<8 $$

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1. For inequality A: $$ v+5 \geq 9 $$ $$ \begin{aligned} v+5 &\geq 9 \ v &\geq 9-5 \ v &\geq 4 \end{aligned} $$ Since the solution set for this inequality is exactly $$ v \geq 4 $$, the inequality is satisfied. 2. For inequality B: $$ v+5 > 9 $$ $$ \begin{aligned} v+5 &> 9 \ v &> 9-5 \ v &> 4 \end{aligned} $$ Here, $$ v = 4 $$ does not satisfy the inequality because $$ 4+5 = 9 $$ is not greater than 9. Thus, $$ v \geq 4 $$ is not a solution to this inequality. 3. For inequality C: $$ v+5 \leq 8 $$ $$ \begin{aligned} v+5 &\leq 8 \ v &\leq 8-5 \ v &\leq 3 \end{aligned} $$ The inequality requires $$ v \leq 3 $$, so any $$ v \geq 4 $$ would not satisfy it. 4. For inequality D: $$ v+5 < 8 $$ $$ \begin{aligned} v+5 &< 8 \ v &< 8-5 \ v &< 3 \end{aligned} $$ This inequality also restricts $$ v $$ to being less than 3, hence $$ v \geq 4 $$ does not satisfy it. Thus, only inequality A has $$ v \geq 4 $$ as a solution. Inequality A ($$ v+5 \geq 9 $$) is the only one where $$ v \geq 4 $$ is a solution.

For which of the inequalities below is \( v \geq 4 \) a solution? A. \( v+5 \geq 9 \) B. \( v+5>9 \) C. \( v+5 \leq 8 \) D. \( v+5<8 \)

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