Inequalities and Their Representations

The video tutorial by JD covers one-variable inequalities, focusing on set-builder notation, graphing on a number line, and interval notation. JD provides three examples to illustrate these concepts, guiding viewers through each step. The tutorial encourages practice and offers clear instructions for each method, ensuring learners understand how to represent inequalities in different forms.

What are the three tasks you need to perform with one variable inequalities?

• Solve equations, write in set-builder notation, and graph on a number line

• Put in set-builder notation, graph on a number line, and write in interval notation

• Solve equations, graph on a number line, and write in interval notation

• Graph on a number line, solve equations, and write in set-builder notation

In set-builder notation, what symbol is used to denote 'such that'?

• Colon (:)

• Semicolon (;)

• Vertical bar (|)

• Comma (,)

How is the inequality X > -3 represented on a number line?

• With an open circle at -3 and shading to the left

• With a closed circle at -3 and shading to the left

• With a closed circle at -3 and shading to the right

• With an open circle at -3 and shading to the right

What is the interval notation for the inequality X > -3?

• [-3, ∞)

• [-3, ∞]

• (-3, ∞]

• (-3, ∞)

In set-builder notation, how is the inequality X ≤ 4 expressed?

• {X | X ≥ 4}

• {X | X > 4}

• {X | X ≤ 4}

• {X | X < 4}

How is the inequality X ≤ 4 represented on a number line?

• With an open circle at 4 and shading to the right

• With a closed circle at 4 and shading to the right

• With an open circle at 4 and shading to the left

• With a closed circle at 4 and shading to the left

What is the interval notation for the inequality X ≤ 4?

• [4, ∞)

• (-∞, 4]

• (4, ∞)

• (-∞, 4)

In set-builder notation, how is the inequality -2 ≤ X < 5 expressed?

• {X | -2 ≤ X < 5}

• {X | -2 < X ≤ 5}

• {X | -2 ≤ X ≤ 5}

• {X | -2 < X < 5}

How is the inequality -2 ≤ X < 5 represented on a number line?

• With open circles at both -2 and 5, shading in between

• With an open circle at -2 and a closed circle at 5, shading in between

• With a closed circle at -2 and an open circle at 5, shading in between

• With closed circles at both -2 and 5, shading in between

What is the interval notation for the inequality -2 ≤ X < 5?

• [-2, 5)

• (-2, 5)

• (-2, 5]

• [-2, 5]