What is a boundary point in the context of solving inequalities?

A boundary point is the value of x that you find when you solve the inequality as if it were an equation. It marks the point on the number line where the solution to the inequality begins or ends.

Explain the difference between using an open dot versus a closed dot on a number line when representing inequalities.

An open dot indicates that the boundary point is not included in the solution set (e.g., ), while a closed dot indicates that the boundary point is included in the solution set (e.g., ≤ or ≥).

Why is it important to test a point that is NOT the boundary point when solving inequalities?

Testing a point helps determine which side of the boundary point contains the solutions that satisfy the inequality.

Solve the inequality 2x + 5 < 11 and represent the solution on a number line. Describe the steps you took.

x 2x = 6 => x = 3. 2. Draw a number line with an open dot at 3. 3. Test a point (e.g., 0): 2(0) + 5 5 < 11 (True). 4. Shade towards the test point (0), so shade to the left of 3.

Solve the inequality -3x ≥ 12 and represent the solution on a number line. Describe the steps you took.

x ≤ -4. Steps: 1. Solve for x as if it were an equation: -3x = 12 => x = -4. 2. Draw a number line with a closed dot at -4. 3. Test a point (e.g., 0): -3(0) ≥ 12 => 0 ≥ 12 (False). 4. Shade away from the test point (0), so shade to the left of -4.

Solving Linear Inequalities Lesson Plan for Grade 9th Grade

Lesson Preview

Learning Objective

I can solve one-step and two-step linear inequalities and represent the solutions on a number line.

1
When solving inequalities, you can temporarily replace the inequality sign with an equal sign to find the boundary point.
2
After finding the boundary point, draw a number line and use an open or closed dot to represent whether the boundary point is included in the solution.
3
To determine which direction to draw the line on the number line, test a point that is not the boundary point in the original inequality; if the statement is true, shade towards the test point, and if it is false, shade away from the test point.

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