Solve the inequality 5v - 14 > 51 for v.
Understand the Problem
The question asks to solve the inequality $5v - 14 > 51$ for the variable $v$. We need to isolate $v$ on one side of the inequality to find the solution set.
Answer
$v > 13$
Answer for screen readers
$v > 13$
Steps to Solve
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Isolate the term with $v$ Add 14 to both sides of the inequality: $$5v - 14 + 14 > 51 + 14$$ $$5v > 65$$
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Solve for $v$ Divide both sides of the inequality by 5: $$\frac{5v}{5} > \frac{65}{5}$$ $$v > 13$$
$v > 13$
More Information
The solution to the inequality $5v - 14 > 51$ is $v > 13$. This means that any value of $v$ greater than 13 will satisfy the original inequality.
Tips
A common mistake is forgetting to perform the same operation on both sides of the inequality. Another common mistake is dividing or multiplying by a negative number without flipping the inequality sign. In this problem, we only added and divided by a positive number, so the inequality sign remained the same.
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