Solving Linear Inequalities in One Variable

This video tutorial covers solving linear inequalities in one variable. It explains the steps involved, highlighting the importance of reversing the inequality symbol when multiplying or dividing by a negative number. The tutorial includes examples demonstrating these concepts, showing how to solve inequalities and graph the solution sets using interval notation.

What is the key difference when solving a linear inequality compared to a linear equation?

• You must always add a constant to both sides.

• You must reverse the inequality symbol when multiplying or dividing by a negative number.

• You must reverse the inequality symbol when adding or subtracting a negative number.

• You must always subtract a constant from both sides.

Why do we need to reverse the inequality symbol when dividing both sides by a negative number?

• Because the inequality symbol always changes direction.

• Because the values on both sides of the inequality become positive.

• Because the inequality would otherwise become false.

• Because the values on both sides of the inequality become negative.

If you divide both sides of the inequality -4 > -8 by -2, what should the new inequality be?

• -2 > -4

• -2 < -4

• 2 < 4

• 2 > 4

In the example 3x > x + 6, what is the first step to isolate the variable x?

• Divide both sides by 3.

• Subtract x from both sides.

• Add x to both sides.

• Multiply both sides by 3.

What is the solution to the inequality 3x > x + 6?

• x < 3

• x > 3

• x < 2

• x > 2

How is the solution x > 3 represented in interval notation?

• (3, ∞)

• [3, ∞]

• [3, ∞)

• (3, ∞]

In the inequality 3 - 5a ≤ 2a + 10, what is the first step to isolate the variable a?

• Add 5a to both sides.

• Subtract 2a from both sides.

• Add 2a to both sides.

• Subtract 5a from both sides.

What is the solution to the inequality -7a ≤ 7 after isolating the variable a?

• a ≥ -1

• a ≤ -1

• a ≤ 1

• a ≥ 1

In the final example, what is the result of dividing both sides of the inequality -2x ≥ -2 by -2?

• x ≥ 1

• x ≥ -1

• x ≤ 1

• x ≤ -1

How is the solution x ≤ 1 represented in interval notation?

• (-∞, 1]

• (1, ∞)

• [1, ∞)

• (-∞, 1)