Question
Solve the inequality and represent your answer using set builder notation.
7-4x < 23
・{-4}
・{x : x < -4}
・4
・{x : x > -4}
Show all work or steps from the problem above to receive full credit. You can type your answer in the box below
7-4x < 23
・{-4}
・{x : x < -4}
・4
・{x : x > -4}
Show all work or steps from the problem above to receive full credit. You can type your answer in the box below
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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:
\[
\{ x : x > -4 \}
\]
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:
\[
\{ x : x > -4 \}
\]
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