Understanding Linear Inequalities

What is the main difference between an equation and an inequality?

• An inequality always has no solution.

• Both have the same number of solutions.

• An equation has a single solution, while an inequality has multiple possible solutions.

• An equation has multiple solutions, while an inequality has a single solution.

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

• Add 4 to both sides.

• Divide both sides by 4.

• Subtract 4 from both sides.

• Multiply both sides by 4.

How is the solution X > -1 represented on a number line?

• With an open circle at -1 and a line extending to the right.

• With a solid circle at -1 and a line extending to the right.

• With an open circle at -1 and a line extending to the left.

• With a solid circle at -1 and a line extending to the left.

What is the interval notation for the solution X > -1?

• [-1, ∞)

• (-∞, -1)

• (-∞, -1]

• (-1, ∞)

In the inequality 3X + 2 ≤ -2, what operation is performed first to isolate X?

• Add 2 to both sides.

• Multiply both sides by 3.

• Divide both sides by 3.

• Subtract 2 from both sides.

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

• With an open circle at 2 and a line extending to the right.

• With a solid circle at 2 and a line extending to the left.

• With a solid circle at 2 and a line extending to the right.

• With an open circle at 2 and a line extending to the left.

What is the interval notation for the solution X ≤ 2?

• [2, ∞)

• (2, ∞)

• (-∞, 2)

• (-∞, 2]

In the inequality -3X + 5 ≤ -19, what must be done after subtracting 5 from both sides?

• Subtract 3 from both sides.

• Add 3 to both sides.

• Divide both sides by -3.

• Multiply both sides by -3.

What happens to the inequality sign when you divide both sides by a negative number?

• It disappears.

• It becomes an equal sign.

• It reverses direction.

• It stays the same.

What is the interval notation for the solution X ≥ 8?

• (-∞, 8]

• [8, ∞)

• (-∞, 8)

• (8, ∞)