Question

Solve the inequality and represent your answer using set builder notation.
7-4x < 23
・{-4}
・{x : x < -4}
・4
・{x : x > -4}
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Answer 1

To solve the inequality \( 7 - 4x < 23 \), we can follow these steps:

1. **Subtract 7 from both sides:**
\[
7 - 4x - 7 < 23 - 7
\]
This simplifies to:
\[
-4x < 16
\]

2. **Divide both sides by -4:**
When we divide by a negative number, we must reverse the inequality sign.
\[
x > \frac{16}{-4}
\]
Simplifying this gives:
\[
x > -4
\]

3. **Represent the solution in set builder notation:**
The solution can be expressed as:
\[
\{ x : x > -4 \}
\]

Thus, the answer is:
\[
\{ x : x > -4 \}
\]