Solving Two-Step Linear Inequalities in One Variable

This video tutorial covers solving two-step linear inequalities in one variable. It explains how to express solutions as inequalities, graphs, and using interval notation. The tutorial provides a review of these methods and demonstrates the steps to solve inequalities, emphasizing the importance of reversing the inequality symbol when multiplying or dividing by a negative number. Several examples are provided, including cases with negative coefficients and variables on the right side, to illustrate the concepts and graphing techniques.

What are the three ways to express the solution of a two-step linear inequality?

• Inequality, table, and interval notation

• Equation, graph, and interval notation

• Inequality, graph, and interval notation

• Equation, table, and graph

When solving a linear inequality, what must you do if you multiply or divide by a negative number?

• Keep the inequality symbol the same

• Subtract a positive number from both sides

• Reverse the inequality symbol

• Add a positive number to both sides

In the inequality 3X + 4 ≥ 10, what is the first step to isolate X?

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 4 from both sides

• Add 4 to both sides

After isolating X in the inequality 3X + 4 ≥ 10, what is the next step?

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 4 from both sides

• Add 4 to both sides

How is the solution X ≥ 2 represented on a number line?

• Open point on 2 with an arrow to the right

• Closed point on 2 with an arrow to the right

• Open point on 2 with an arrow to the left

• Closed point on 2 with an arrow to the left

In the inequality -2X - 1 > 9, what is the first step to isolate X?

• Add 1 to both sides

• Divide both sides by -2

• Subtract 1 from both sides

• Multiply both sides by -2

When dividing both sides of -2X > 10 by -2, what must you remember to do?

• Keep the inequality symbol the same

• Subtract 2 from both sides

• Reverse the inequality symbol

• Add 2 to both sides

How is the solution X < -5 represented on a number line?

• Closed point on -5 with an arrow to the right

• Open point on -5 with an arrow to the right

• Open point on -5 with an arrow to the left

• Closed point on -5 with an arrow to the left

In the inequality 12 ≥ -3X, what is the first step to isolate X?

• Divide both sides by -3

• Subtract 3 from both sides

• Multiply both sides by -3

• Add 3 to both sides

How is the solution X > -4 represented in interval notation?

• [-∞, -4]

• (-∞, -4)

• [-4, ∞)

• (-4, ∞)