Question

q3 - accelerated mathematics gr 8 | lesson: solving and graphing linear inequalities in one-variable

1. which statement correctly describes the graph of $x \geq 2$

a. closed circle at 2, shading to the right
b. closed circle at 2, shading to the left
c. open circle at 2, shading to the left
d. open circle at 2, shading to the right

1. which of the following inequalities is represented by a number line with an open circle at 4 and shading to the right?

a. $x \geq 4$
b. $x \leq 4$
c. $x < 4$
d. $x > 4$

1. what is the correct graph for the inequality $3 \geq x$

a. open circle at 3 with shading to the left
b. closed circle at 3 with shading to the left
c. closed circle at 3 with shading to the right
d. open circle at 3 with shading to the right

1. which of the following describes an inequality solved by adding 2 to both sides?

Explanation:

Step1: Analyze $x \geq 2$ graph rules

For $\geq$, use closed circle at 2; values greater than 2 are to the right, so shade right.

Step2: Analyze open circle at 4, shade right

Open circle means $>$ or $<$, shade right means values greater than 4, so inequality is $x > 4$.

Step3: Rewrite $3 \geq x$ as $x \leq 3$

For $\leq$, use closed circle at 3; values less than 3 are to the left, so shade left.

Answer:

1. a. Closed circle at 2, shading to the right
2. d. $x > 4$
3. b. Closed circle at 3 with shading to the left