Solving Inequalities with Fractions and Absolute Values

This video tutorial covers graphing and solving inequalities on number lines, including those with fractions, variables on both sides, and absolute values. It explains how to represent solutions in interval notation and provides step-by-step examples for each type of inequality. The tutorial also addresses compound inequalities and demonstrates how to solve them efficiently.

How do you represent the inequality x > 2 on a number line?

• Open circle at 2, shade to the right

• Closed circle at 2, shade to the left

• Open circle at 2, shade to the left

• Closed circle at 2, shade to the right

Tags

CCSS.6.EE.B.8

What is the interval notation for x ≥ -1?

• [-1, ∞)

• (-1, ∞)

• (-∞, -1)

• (-∞, -1]

Tags

CCSS.6.EE.B.8

How do you represent x < 4 on a number line?

• Closed circle at 4, shade to the right

• Open circle at 4, shade to the right

• Closed circle at 4, shade to the left

• Open circle at 4, shade to the left

Tags

CCSS.6.EE.B.8

What is the interval notation for x ≤ -2?

• (-2, ∞)

• (-∞, -2]

• (-∞, -2)

• [-2, ∞)

Tags

CCSS.7.EE.B.4B

How do you solve the inequality x + 4 > 5?

• Divide both sides by 4

• Multiply both sides by 4

• Add 4 to both sides

• Subtract 4 from both sides

Tags

CCSS.7.EE.B.4B

What is the solution to the inequality 7 - 2x ≤ 12?

• x ≥ -2.5

• x ≤ -2.5

• x ≤ 2.5

• x ≥ 2.5

How do you solve the inequality 4 - 2x ≥ 3x + 19?

• Add 2x to both sides

• Divide both sides by 2

• Subtract 4 from both sides

• Subtract 3x from both sides

Tags

CCSS.6.EE.B.8

What is the interval notation for x ≤ -3?

• (-3, ∞)

• [-3, ∞)

• (-∞, -3)

• (-∞, -3]

How do you solve the absolute value inequality |x| < 4?

• x < 4 and x > -4

• x < 4 or x > -4

• x > 4 and x < -4

• x > 4 or x < -4

What is the solution to the inequality 5 - 3|4x + 1| ≥ -9?

• x ≥ 5.5 or x ≤ -2.5

• x ≥ 5.5 and x ≤ -2.5

• x ≤ 5.5 or x ≥ -2.5

• x ≤ 5.5 and x ≥ -2.5