Question

related questions: lesson 5: inequalities

select the option that is true for the graph at 0.

q. solve and graph the equation.

(0 > -7x ge -7)

Explanation:

Separate the compound inequality

Using the Solving Linear Inequalities knowledge point

$$ 0 > -7x \quad \text{and} \quad -7x \ge -7 $$

Solve the first inequality

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK0
$$

Solve the second inequality

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK1
$$

Combine the solution sets

Using the Inequality Solution Sets knowledge point

$$ 0 < x \le 1 $$

Analyze the graph at 0

We examine the boundary point at \(x = 0\). Since the inequality is strict (\(x > 0\)), the value \(0\) is not included in the solution set. On a number line graph, this is represented by an open circle (or open dot) at \(0\).

Answer:

The solution to the compound inequality is \(0 < x \le 1\).

For the graph at \(0\), the correct option is:
An open circle (or open dot) at 0