Question

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Part 1
Solve the inequality. Write the solution in​ set-builder notation.
negative 3 x minus 8 less than or equals minus 23
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Part 1
The solutions are given by​ {x |
  
enter your response here​}.
​(Type an inequality. Use integers or fractions for any numbers in the expression. Simplify your​ answer.)

Answer 1

To solve the inequality \(-3x - 8 \leq -23\), follow these steps:

1. **Isolate the term involving \(x\)**. Start by adding 8 to both sides:
\[
-3x - 8 + 8 \leq -23 + 8
\]
This simplifies to:
\[
-3x \leq -15
\]

2. **Divide by \(-3\)**. Remember that when you divide or multiply both sides of an inequality by a negative number, the inequality sign flips:
\[
x \geq 5
\]

Thus, the solution in set-builder notation is:
\[
\{ x \mid x \geq 5 \}
\]