Understanding Inequalities and Graphing

The video tutorial covers solving inequalities and graphing their solutions. It begins with solving inequalities by isolating the variable and choosing the correct graph representation. The tutorial includes examples, such as spending limits, to illustrate graphing on a number line. It also emphasizes checking if graphs match inequalities and performing error analysis to identify common mistakes. The tutorial aims to enhance understanding of inequalities and their graphical representation.

What is the first step in solving the inequality 49 ≥ x + 22?

• Multiply both sides by 22

• Subtract 22 from both sides

• Divide both sides by 22

• Add 22 to both sides

When graphing the solution x ≤ 27, what should be done at 27 on the number line?

• Draw an open circle

• Draw a closed circle

• Shade to the left

• Shade to the right

If Miss Henry can spend no more than $17, which inequality represents this situation?

• x ≤ 17

• x ≥ 17

• x < 17

• x > 17

In the context of graphing inequalities, what does a closed circle on a number line indicate?

• The number is not included in the solution

• The number is included in the solution

• The inequality is not strict

• The inequality is strict

What is the inverse operation of multiplying by 3?

• Adding 3

• Subtracting 3

• Dividing by 3

• Multiplying by 3

What does the inequality x + 5 ≤ 11 simplify to?

• x ≤ 6

• x > 6

• x ≥ 6

• x < 6

Which of the following is a correct representation of the inequality x > 20?

• x > 20

• x ≥ 20

• x ≤ 20

• x < 20

What mistake did Perry make when graphing the inequality 5x < 10?

• He used a closed circle instead of an open circle

• He used the wrong inequality symbol

• He included the number 5 in the solution

• He shaded the wrong side of the number line

If John has fewer than 30 marbles, which inequality represents this?

• n > 30

• n < 30

• n ≤ 30

• n ≥ 30

How should the number 30 be represented on a number line for the inequality n < 30?

• With a closed circle

• With an open circle

• With a shaded circle

• With no circle