Solve the inequality for v: 42 < v/4 + 16. Simplify your answer as much as possible.
Understand the Problem
The problem requires solving an inequality for the variable 'v'. Specifically, we need to isolate 'v' in inequality (42 < \frac{v}{4} + 16) and simplify the answer as much as possible.
Answer
$v > 104$
Answer for screen readers
$v > 104$
Steps to Solve
- Isolate the term with $v$ by subtracting 16 from both sides
We start with the given inequality: $42 < \frac{v}{4} + 16$
Subtract 16 from both sides: $42 - 16 < \frac{v}{4} + 16 - 16$ $26 < \frac{v}{4}$
- Solve for $v$ by multiplying both sides by 4
To isolate $v$, multiply both sides of the inequality by 4: $26 \cdot 4 < \frac{v}{4} \cdot 4$ $104 < v$
- Rewrite the inequality with $v$ on the left side
We can rewrite the inequality so that $v$ is on the left, remembering to flip the inequality sign: $v > 104$
$v > 104$
More Information
The solution to the inequality $42 < \frac{v}{4} + 16$ is $v > 104$. This means any value of $v$ greater than 104 will satisfy the original inequality.
Tips
A common mistake is forgetting to flip the inequality sign when multiplying or dividing by a negative number. However, in this case since we are multiplying by a positive number, there is no need to flip the inequality sign. Another common mistake is performing the arithmetic incorrectly.
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