Graphing Linear Inequalities on a Number Line

Mr. Allen teaches how to solve and graph inequalities on a number line. He starts with basic inequalities, explaining how to undo subtraction and multiplication. He then demonstrates graphing these inequalities using open circles. The lesson progresses to more complex inequalities involving distribution and combining like terms, emphasizing the importance of flipping the inequality sign when dividing by a negative number. The video concludes with graphing these complex inequalities using closed circles.

What is the first step to solve the inequality 3x - 4 < 11?

• Multiply both sides by 3

• Add 4 to both sides

• Divide both sides by 3

• Subtract 4 from both sides

After adding 4 to both sides of the inequality 3x - 4 < 11, what is the resulting inequality?

• 3x < 7

• 3x < 15

• 3x > 7

• 3x > 15

What is the final solution to the inequality 3x - 4 < 11?

• x < 3

• x > 3

• x < 5

• x > 5

How is the inequality x < 5 represented on a number line?

• Closed circle at 5, shading to the left

• Open circle at 5, shading to the right

• Open circle at 5, shading to the left

• Closed circle at 5, shading to the right

What is the first step in solving the inequality -2(x + 1) - 3 ≥ 7?

• Divide both sides by -2

• Distribute the -2

• Add 3 to both sides

• Subtract 3 from both sides

After distributing -2 in the inequality -2(x + 1) - 3 ≥ 7, what is the resulting inequality?

• -2x - 2 - 3 ≥ 7

• -2x + 2 + 3 ≥ 7

• -2x - 2 + 3 ≥ 7

• -2x + 2 - 3 ≥ 7

What is the next step after combining like terms in the inequality -2x - 5 ≥ 7?

• Divide both sides by -2

• Add 5 to both sides

• Multiply both sides by -2

• Subtract 5 from both sides

What is the final solution to the inequality -2x - 5 ≥ 7?

• x ≥ 6

• x ≤ 6

• x ≥ -6

• x ≤ -6

How is the inequality x ≤ -6 represented on a number line?

• Open circle at -6, shading to the right

• Closed circle at -6, shading to the right

• Closed circle at -6, shading to the left

• Open circle at -6, shading to the left

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

• You add the negative number to both sides

• The inequality sign flips

• You subtract the negative number from both sides

• The inequality sign stays the same