Question

solve the inequality. graph the solution.(describe the graph, open or closed circle then which way the graph is colored)
3s + 5 ≤ -3 or 6s - 5 ≥ 7

Explanation:

Step1: Solve \(3s + 3 \leq -3\)

Subtract 3 from both sides: \(3s + 3 - 3 \leq -3 - 3\)
Simplify: \(3s \leq -6\)
Divide by 3: \(s \leq -2\)

Step2: Solve \(6s - 3 \geq 7\)

Add 3 to both sides: \(6s - 3 + 3 \geq 7 + 3\)
Simplify: \(6s \geq 10\)
Divide by 6: \(s \geq \frac{10}{6} = \frac{5}{3}\)

Step3: Analyze the solution set

The solution is \(s \leq -2\) or \(s \geq \frac{5}{3}\).

For \(s \leq -2\): Closed circle at \(-2\) (since \(\leq\)), shade left.
For \(s \geq \frac{5}{3}\): Closed circle at \(\frac{5}{3}\) (since \(\geq\)), shade right.

Answer:

The solution to the inequality is \(s \leq -2\) or \(s \geq \frac{5}{3}\). The graph has a closed circle at \(-2\) (shaded left) and a closed circle at \(\frac{5}{3}\) (shaded right).