Question
For each inequality, choose the statement that describes its solution. If applicable, give the solution. (a) \( 4(6-u)+4 u<23 \) No solution u< \( u>\square \) All real numbers are solutions
Ask by Grant Barker. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There is no solution to the inequality.
Solution
Let's solve the inequality step by step:
\[
4(6 - u) + 4u < 23
\]
1. **Distribute the 4:**
\[
4 \times 6 - 4 \times u + 4u < 23
\]
\[
24 - 4u + 4u < 23
\]
2. **Combine like terms:**
\[
24 + (-4u + 4u) < 23
\]
\[
24 + 0 < 23
\]
\[
24 < 23
\]
3. **Evaluate the inequality:**
\[
24 < 23
\]
This statement is **false**.
Since the inequality simplifies to a false statement regardless of the value of \( u \), there is **no solution** to the inequality.
**Answer:**
**No solution**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve the inequality \( 4(6-u)+4u<23 \), we start by simplifying it: \( 24 - 4u + 4u < 23 \), which simplifies to \( 24 < 23 \). This statement is false, so there are no values of \( u \) that can satisfy this inequality. Thus, the solution is that there is no solution. When faced with inequalities, it’s essential to manipulate them carefully while keeping track of the operations. A common mistake is neglecting to distribute or combine like terms correctly, which can lead to erroneous conclusions. Always double-check your steps!
