Understanding and Solving Linear Inequalities

The video tutorial explains how to solve and graph a linear inequality, emphasizing the importance of reversing the inequality symbol when multiplying or dividing by a negative number. It demonstrates the process of distributing terms, combining like terms, and isolating the variable to solve the inequality. The solution is expressed as an inequality, graphed on a number line, and written in interval notation. The tutorial concludes with a visual representation of the solution and a brief explanation of interval notation.

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

• Add the same number to both sides

• Reverse the inequality symbol

• Multiply by a positive number

• Subtract the same number from both sides

What is the first step in solving the inequality 3(x + 5) - 8 > x - 1?

• Combine like terms

• Add 8 to both sides

• Distribute the 3

• Subtract x from both sides

After distributing and simplifying, what should you do next to solve 3x + 7 > x - 1?

• Multiply both sides by 2

• Subtract x from both sides

• Divide both sides by 3

• Add x to both sides

What operation should be performed first when solving 2x + 7 > -1?

• Add 7 to both sides

• Subtract 7 from both sides

• Divide by 2

• Multiply by 2

What is the solution to the inequality 2x > -8 after dividing both sides by 2?

• x < -4

• x ≥ -4

• x > -4

• x = -4

How is the solution x > -4 represented on a number line?

• A closed point on -4 with an arrow to the left

• An open point on -4 with an arrow to the left

• An open point on -4 with an arrow to the right

• A closed point on -4 with an arrow to the right

In interval notation, how is the solution x > -4 expressed?

• [-4, ∞)

• (-4, ∞)

• (-4, ∞]

• [-4, ∞]

Why is an open parenthesis used in interval notation for -4 in the solution x > -4?

• Because the interval is infinite

• Because -4 is included in the interval

• Because -4 is not included in the interval

• Because the interval is finite

What does the arrow to the right on the number line indicate in the graph of x > -4?

• Values less than -4

• Values equal to -4

• Values greater than -4

• Values less than or equal to -4

What is the significance of using parentheses around infinity in interval notation?

• Infinity is not included in the interval

• Infinity is a negative number

• Infinity is included in the interval

• Infinity is a finite number