Question

1. which graph shows x < 4?

a. open circle at 4, shading left
b. closed circle at 4, shading left
c. open circle at 4, shading right
d. closed circle at 4, shading right

1. which inequality matches this graph:

closed circle at 10, shading left
a. x < 10
b. x ≤ 10
c. x > 10
d. x ≥ 10

1. check if x = -2 satisfies 2x + 4 ≤ 0.

Explanation:

Step1: Analyze inequality symbols and graphing rules

For inequalities, an open circle is used when the inequality is \(<\) or \(>\) (not including the boundary value), and a closed circle is used when the inequality is \(\leq\) or \(\geq\) (including the boundary value). Shading to the left on a number - line corresponds to values less than the boundary value, and shading to the right corresponds to values greater than the boundary value.

For problem 7:

• The inequality \(x < 4\) means the value \(4\) is not included (so use an open circle) and we consider values less than \(4\) (shading to the left).

For problem 9:

• A closed circle at \(10\) means the value \(10\) is included in the solution set (so the inequality symbol is \(\leq\) or \(\geq\)). Shading to the left means we are looking at values less than or equal to \(10\).

For problem 11:

• Substitute \(x=-2\) into the inequality \(2x + 4\leq0\).
• Calculate the left - hand side: \(2(-2)+4\).
• Using the order of operations (first multiplication: \(2\times(-2)=-4\)), then addition: \(-4 + 4=0\).
• Since \(0\leq0\) is a True statement.

Answer:

• Problem 7: A. Open circle at 4, shading left
• Problem 9: B. \(x\leq10\)
• Problem 11: Yes, \(x = - 2\) satisfies \(2x+4\leq0\)