Understanding and Solving Linear Inequalities

This video tutorial covers the basics of solving and graphing linear inequalities. It explains the use of inequality symbols, how to graph inequalities on a number line, and how to represent solutions using interval notation. The tutorial also provides step-by-step instructions for solving simple and multi-step inequalities, as well as compound inequalities. Key concepts include understanding inequality symbols, graphing techniques, and solving strategies.

Which symbol correctly represents the relationship between -5 and -8?

• =

• >

• <

• ≤

How would you graph the inequality x > 3 on a number line?

• Closed circle at 3, shade to the right

• Open circle at 3, shade to the left

• Open circle at 3, shade to the right

• Closed circle at 3, shade to the left

What is the interval notation for x ≤ -3?

• (-3, ∞)

• [-3, ∞)

• (-∞, -3]

• (-∞, -3)

In a compound inequality, what does the statement -1 < x ≤ 4 mean?

• x is greater than -1 and less than 4

• x is between -1 and 4, excluding both

• x is less than -1 and greater than 4

• x is between -1 and 4, including 4

How do you solve the inequality x + 4 > 9?

• Subtract 4 from both sides

• Multiply both sides by 4

• Divide both sides by 4

• Add 4 to both sides

What is the solution to the inequality 3x > 18?

• x ≤ 6

• x = 6

• x > 6

• x < 6

When solving -2/3x < 12, what is the first step?

• Divide both sides by -2

• Multiply both sides by 3

• Multiply both sides by -3

• Add 2/3 to both sides

How do you solve the inequality 4x + 3 < 7x - 9?

• Subtract 4x from both sides

• Add 7x to both sides

• Subtract 7x from both sides

• Add 4x to both sides

What is the solution to the inequality 5x - 3/4 < 3x - 7/3?

• Multiply both sides by 12

• Subtract 3x from both sides

• Add 3/4 to both sides

• Cross multiply the fractions

In a compound inequality with three sides, what must you do to maintain balance?

• Adjust the left and right sides

• Only adjust the middle side

• Adjust all three sides equally

• Only adjust the left side