Understanding Linear Inequalities

The video tutorial explains how to solve a linear inequality by distributing terms, combining like terms, and isolating the variable. It emphasizes the importance of reversing the inequality symbol when multiplying or dividing by a negative number. The solution is presented as an inequality, graphed on a number line, and expressed using interval notation. The tutorial also covers converting improper fractions to mixed numbers for graphing purposes.

What is a key difference between solving linear equations and inequalities?

• You must always subtract a constant from both sides.

• You must always add a constant to both sides.

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

• You must reverse the inequality symbol when adding a positive number.

What is the result of distributing 3 in the expression 3(x - 9)?

• 3x + 27

• 3x - 27

• 3x - 9

• 3x + 9

After combining like terms, what is the simplified form of 3x - 27 - 2?

• 3x - 25

• 3x - 29

• 3x - 30

• 3x - 28

How do you eliminate the -4x on the right side of the inequality?

• Divide both sides by 4

• Add 4x to both sides

• Subtract 4x from both sides

• Multiply both sides by 4

What is the final step to solve for x in the inequality 7x ≤ 20?

• Divide both sides by 7

• Multiply both sides by 7

• Subtract 7 from both sides

• Add 7 to both sides

When graphing x ≤ 27/7 on a number line, what type of point is used at 27/7?

• Closed point

• Open point

• Dashed point

• Arrow point

What is the mixed number form of 27/7?

• 2 and 5/7

• 4 and 6/7

• 2 and 6/7

• 3 and 6/7

In interval notation, how is the solution x ≤ 27/7 expressed?

• (-∞, 27/7]

• (27/7, ∞)

• (-∞, 27/7)

• [27/7, ∞)

Why do we use a square bracket in the interval notation for x ≤ 27/7?

• Because 27/7 is not included in the solution

• Because 27/7 is included in the solution

• Because the interval is infinite

• Because the interval is finite

What symbol is used to represent negative infinity in interval notation?

• Angle bracket

• Rounded parenthesis

• Curly brace

• Square bracket