Solving Linear Inequalities in One Variable

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)