Linear Inequalities and Their Solutions

This video tutorial covers solving two-step linear inequalities in one variable. It explains the process of solving these inequalities, including reversing the inequality symbol when multiplying or dividing by a negative number. The tutorial provides examples of expressing solutions as inequalities, graphs, and using interval notation. It also demonstrates solving inequalities with variables on the right side and emphasizes the importance of correctly graphing and using interval notation.

What are the three ways to express the solutions of two-step linear inequalities?

• As a fraction, a decimal, and a percentage

• As an inequality, a graph, and using interval notation

• As a polynomial, a graph, and using set notation

• As a matrix, a graph, and using vector notation

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

• Subtract a constant from both sides

• Add a constant to both sides

• Keep the inequality symbol the same

• Reverse the inequality symbol

In the example 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

What is the interval notation for the solution x ≥ 2?

• (2, ∞]

• [2, ∞)

• (2, ∞)

• [2, ∞]

In the inequality -2x - 1 > 9, what operation is performed after adding 1 to both sides?

• Divide by -2

• Multiply by 2

• Multiply by -2

• Divide by 2

What is the graph representation for the solution x < -5?

• Open point on -5 with arrow to the right

• Closed point on -5 with arrow to the left

• Open point on -5 with arrow to the left

• Closed point on -5 with arrow to the right

In the example 12 ≥ -3x, what is the result after dividing both sides by -3?

• x ≤ 4

• x ≥ 4

• x ≥ -4

• x ≤ -4

How is the inequality x > -4 represented in interval notation?

• (-4, ∞)

• (-∞, -4]

• [-4, ∞)

• (-∞, -4)

What is the correct graph representation for x > -4?

• Closed point on -4 with arrow to the left

• Open point on -4 with arrow to the left

• Closed point on -4 with arrow to the right

• Open point on -4 with arrow to the right

In the inequality -20 > 5x, what is the solution for x after dividing by 5?

• x ≥ -4

• x ≤ -4

• x > -4

• x < -4