# Solving Inequalities

Videos and solutions to help Algebra I students learn the process of solving inequalities.

New York State Common Core Math Module 1, Algebra I, Lesson 14

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Common Core For Algebra I

Lesson 14 Student Outcomes

Students learn if-then moves using the addition and multiplication properties of inequality to solve inequalities and graph the solution sets on the number line.

Properties of Inequality

Recall the Properties of Inequality:

If A > B, then A + c > B + c for any real number c.

Multiplication property of inequality:

If A > B, then kA > kB for any positive real number k.

Exit Ticket

1. Find the solution set to each inequality. Express the solution in set notation and graphically on the number line.

a. 6x + 2 < 7x - 1

b. x2 + 2(x - 1) ≥ x2 + 5

2. Fergus was absent for today’s lesson and asked Mike to explain why the solution to -5x > 30 is x < -6. Mike said, “Oh! That’s easy. When you multiply by a negative, just flip the inequality.” Provide a better explanation to Fergus about why the direction of the inequality is reversed.

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