Question
1-4, solve each inequality. \( \begin{array}{ll}\text { 2. } 3.5+4 t \leq 39.5\end{array} \)
Ask by Davey Goodwin. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( t \leq 9 \)
Solution
Sure, let's solve inequality **2.** step by step.
**Given Inequality:**
\[
3.5 + 4t \leq 39.5
\]
**Step 1: Subtract 3.5 from both sides to isolate the term with \( t \).**
\[
4t \leq 39.5 - 3.5
\]
\[
4t \leq 36
\]
**Step 2: Divide both sides by 4 to solve for \( t \).**
\[
t \leq \frac{36}{4}
\]
\[
t \leq 9
\]
**Solution:**
\[
t \leq 9
\]
**Interpretation:**
Any real number \( t \) that is less than or equal to 9 satisfies the inequality.
**Graphical Representation:**
\[
(-\infty, 9]
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve the inequality \(3.5 + 4t \leq 39.5\), start by isolating the term with \(t\). Subtract 3.5 from both sides: \[ 4t \leq 39.5 - 3.5 \] This simplifies to: \[ 4t \leq 36 \] Now, divide both sides by 4: \[ t \leq 9 \] So the solution to the inequality is \(t \leq 9\). Want to test your solution? Pick a value for \(t\) that fits the inequality, such as \(t = 8\). Substitute it back to check: \[ 3.5 + 4(8) = 3.5 + 32 = 35.5 \leq 39.5 \text{ (True)} \] Now try \(t = 10\): \[ 3.5 + 4(10) = 3.5 + 40 = 43.5 \leq 39.5 \text{ (False)} \] You see? \(t = 8\) is correct, while \(t = 10\) doesn't satisfy the inequality—making \(t \leq 9\) the right range!
