Question
Solve the inequality for \( v \). \[ \frac{v}{4}>7 \]
Ask by Mccarthy Tucker. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( v > 28 \)
Solution
To solve the inequality:
\[
\frac{v}{4} > 7
\]
**Step 1: Eliminate the Denominator**
Multiply both sides of the inequality by 4 to isolate \( v \). Since 4 is a positive number, the direction of the inequality remains the same.
\[
\frac{v}{4} \times 4 > 7 \times 4
\]
\[
v > 28
\]
**Solution:**
\[
v > 28
\]
**Interval Notation:**
\[
v \in (28, \infty)
\]
This means that \( v \) can be any real number greater than 28.
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Simplify this solution Extra Insights
To solve the inequality \( \frac{v}{4} > 7 \), you can start by eliminating the fraction. Multiply both sides of the inequality by 4: \[ v > 7 \times 4 \] This simplifies to: \[ v > 28 \] So the solution to the inequality is \( v > 28 \). The critical part here is always to remember that when you multiply or divide an inequality by a negative number, you must flip the inequality sign! Luckily, in this case, we weren't multiplying or dividing by a negative, so we keep the inequality as it is. Keep an eye out for that little detail!
