Mastering Inequalities

Q1. What is the comparison operator for greater than?

• greater than

• less than

• less than or equal to

• greater than or equal to

greater than less than less than or equal to greater than or equal to

• greater than

• less than

• less than or equal to

• greater than or equal to

Q1. What is the comparison operator for greater than?

• greater than

• less than

• less than or equal to

• greater than or equal to

Charlotte and Zoe are having a friendly debate about graphing inequalities. They come across the inequality: y<5 When they graph this inequality, what kind of circle should they use to represent it?

• open circle

• closed circle

Answer explanation

The inequality y < 5 indicates that y can take any value less than 5, but not equal to 5. Therefore, when graphed, it will be represented with an open circle at (5) to show that 5 is not included in the solution.

Hey there, math adventurer! Imagine you're on a quest with Liam and Mia to solve the mystery of the inequality. When you graph the inequality 2 > f, what magical symbol will appear on the number line?

• open circle

• closed circle

Answer explanation

The inequality 2 > f indicates that f can take any value less than 2. When graphed, the point at f = 2 will be represented with a closed circle, indicating that 2 is not included in the solution set.

Noah and Kai are on a treasure hunt! They need to find the secret path marked on the number line. Can you help them by writing an inequality for the graph?

Answer explanation

The graph indicates that values of x are less than or equal to -2, which corresponds to the inequality x ≤ -2. This includes -2 itself, making it the correct choice.

• x ≤ 3 and x > -2

• x < -2 or x ≥ 3

• x > -2 or x < 3

• x < 3 and x ≥ -2

• x > -3 or x > 1

• x < -3 or x < 1

• x ≥ 3 and x ≤ 1

• x > -3 and x < 1

Answer explanation

To solve the inequality 2x + 3 ≤ 11, subtract 3 from both sides to get 2x ≤ 8. Then, divide by 2 to find x ≤ 4. Thus, the correct choice is x ≤ 4.

Answer explanation

To solve |x - 4| < 3, we split it into two inequalities: -3 < x - 4 < 3. This simplifies to 1 < x < 7, which matches the correct choice.