Question
Solve. Write your answer interval and set notation. \( -7 a-11<1-4 a \) Solution Interval Notation Set Notation
Ask by Erickson Rodriguez. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( a > -4 \)
Interval Notation: \( (-4, \infty) \)
Set Notation: \( \{ a \mid a > -4 \} \)
Solution
To solve the inequality:
\[
-7a - 11 < 1 - 4a
\]
**Step-by-Step Solution:**
1. **Bring all terms containing \( a \) to one side and constant terms to the other side.**
Add \( 7a \) to both sides:
\[
-7a - 11 + 7a < 1 - 4a + 7a
\]
Simplifies to:
\[
-11 < 1 + 3a
\]
2. **Isolate the term with \( a \).**
Subtract \( 1 \) from both sides:
\[
-11 - 1 < 3a
\]
Simplifies to:
\[
-12 < 3a
\]
3. **Solve for \( a \).**
Divide both sides by \( 3 \):
\[
\frac{-12}{3} < a
\]
Simplifies to:
\[
-4 < a
\]
Which can also be written as:
\[
a > -4
\]
**Final Answer:**
- **Interval Notation:**
\[
(-4, \infty)
\]
- **Set Notation:**
\[
\{\, a \mid a > -4 \,\}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the inequality \( -7a - 11 < 1 - 4a \), first, we rearrange the terms to isolate \(a\). Adding \(7a\) and \(11\) to both sides gives: \( 0 < 1 + 3a + 11 \) This simplifies to: \( 0 < 12 + 3a \) Now, subtracting 12 from both sides results in: \( -12 < 3a \) Dividing by 3 yields: \( -4 < a \) Thus, the solution in interval notation is: \( (-4, \infty) \) In set notation, it is expressed as: \{a | a > -4\}.
