Question

do you remember? solving and graphing a one - variable inequality
a) solve the inequality - 2x + 3 ≤ 9 for x.
b) graph the solution set on a number line.
how do you determine which direction the graph goes?
how do you know what type of circle to place on the number line?

Explanation:

Step1: Isolate the variable term

Subtract 3 from both sides of -2x + 3 ≤ 9:
-2x+3 - 3≤9 - 3
-2x≤6

Step2: Solve for x

Divide both sides by - 2. When dividing an inequality by a negative number, the direction of the inequality sign changes.
$\frac{-2x}{-2}\geq\frac{6}{-2}$
x≥ - 3

Step3: Graph - explanation for direction

Since x≥ - 3, the values of x include - 3 and all numbers greater than - 3. So the graph goes to the right[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]

Answer:

Step1: Isolate the variable term

Subtract 3 from both sides of -2x + 3 ≤ 9:
-2x+3 - 3≤9 - 3
-2x≤6

Step2: Solve for x

Divide both sides by - 2. When dividing an inequality by a negative number, the direction of the inequality sign changes.
$\frac{-2x}{-2}\geq\frac{6}{-2}$
x≥ - 3

Step3: Graph - explanation for direction

Since x≥ - 3, the values of x include - 3 and all numbers greater than - 3. So the graph goes to the right[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]