Question
Which of the following is a solution to the inequality below? \[ \begin{array}{l}1+d>4 \\ \qquad d=2 \\ \text { Submit }\end{array} \]
Ask by Nunez Chen. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(d=2\) is not a solution to the inequality \(1+d>4\).
Solution
We start with the inequality:
\[
1+d>4.
\]
**Step 1. Solve the inequality for \(d\):**
Subtract \(1\) from both sides:
\[
1+d-1>4-1,
\]
which simplifies to:
\[
d>3.
\]
**Step 2. Analyze the given candidate \(d=2\):**
The candidate provided is \(d=2\). Since the inequality requires that \(d>3\), we check:
\[
2>3,
\]
which is false.
**Conclusion:**
The candidate \(d=2\) is not a solution to the inequality. The solution to the inequality is any number greater than \(3\).
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Simplify this solution Mind Expander
To check if \( d = 2 \) is a solution to the inequality \( 1 + d > 4 \), we substitute \( d \) into the inequality. Calculating, we have: \[ 1 + 2 > 4 \] which simplifies to: \[ 3 > 4 \] This statement is false, meaning \( d = 2 \) is not a solution to the inequality. If you're solving inequalities, it's always slightly different than just equations; be mindful of the signs and what they mean for the values! A common mistake is assuming the original statement holds true without verifying after substituting.
