Solving Linear Inequalities in One Variable

This video tutorial by Mr. Backett Work covers solving linear inequalities in one variable. It begins with an introduction to linear inequalities and the various inequality symbols. The video then explains how to perform operations such as addition, subtraction, multiplication, and division on inequalities, highlighting the importance of flipping the inequality sign when multiplying or dividing by a negative number. Several examples are provided, including solving linear inequalities, dealing with fractions, and handling double-sided inequalities. The video concludes with writing solutions in interval notation.

Which of the following is NOT an inequality symbol?

• <

• >

• =

• ≤

If you have the inequality X - 7 > 4, what operation would you use to isolate X?

• Multiply both sides by 7

• Add 7 to both sides

• Divide both sides by 7

• Subtract 7 from both sides

When solving the inequality Z + 3 ≤ 9, what is the resulting inequality after isolating Z?

• Z ≤ 6

• Z ≥ 6

• Z > 6

• Z < 6

What must you remember to do when multiplying or dividing both sides of an inequality by a negative number?

• Add the same number to both sides

• Subtract the same number from both sides

• Keep the inequality symbol the same

• Flip the inequality symbol

In the inequality 2X < 7, what is the value of X after isolating it?

• X < 3.5

• X > 3.5

• X ≤ 3.5

• X ≥ 3.5

What is the first step in solving the inequality 3(X - 1) + 2 ≤ 5X + 6?

• Add 1 to both sides

• Combine like terms

• Distribute the 3

• Subtract 2 from both sides

After solving the inequality 3(X - 1) + 2 ≤ 5X + 6, what is the final value of X?

• X ≥ -3.5

• X < -3.5

• X ≤ -3.5

• X > -3.5

When dealing with fractions in inequalities, what is the first step?

• Add the fractions

• Multiply the fractions

• Find the least common denominator

• Subtract the fractions

In the inequality involving fractions, what is the least common denominator for the denominators 2, 3, 4, and 3?

• 6

• 12

• 8

• 10

In a double-sided inequality, what must you do to both sides when you multiply or divide by a number?

• Subtract the number from both sides

• Add the number to both sides

• Only multiply or divide one side

• Multiply or divide both sides