Understanding Linear Inequalities

Answer explanation

The inequality x < -3 means that x is less than -3. This can be rewritten as -3 > x, which is equivalent. Therefore, the correct choice is -3 > x.

Which of the following inequalities represents the condition: "A number is at most 7"?

Answer explanation

The phrase "at most 7" means the number can be 7 or any number less than 7. This is represented by the inequality x ≤ 7, which includes 7 itself. Therefore, the correct choice is x ≤ 7.

• A person must be at least 10 years old to enter the amusement park.

• A person must be younger than 10 years old to enter the amusement park.

• A person must be exactly 10 years old to enter the amusement park.

• A person must be older than 10 years old to enter the amusement park.

Answer explanation

The inequality x ≥ 10 indicates that a person must be at least 10 years old to enter the amusement park, making the first choice the correct one.

• 6

• 5

• 4

• 7

Answer explanation

The inequality x < 5 means x can be any number less than 5. Among the choices, 4 is less than 5, making it part of the solution set. The other options (5, 6, and 7) are not less than 5.

• -3

• -2

• -4

• -5

Answer explanation

The inequality x ≥ -2 is true for any number greater than or equal to -2. Among the choices, -2 is the only number that satisfies this condition, as -3, -4, and -5 are all less than -2.

Answer explanation

The inequality x ≤ 0 means x is less than or equal to 0. This can be rewritten as 0 ≥ x, which is equivalent. The other options do not represent the same relationship.

Write a linear inequality to represent the condition: "A number is greater than or equal to 12."

Answer explanation

The condition "A number is greater than or equal to 12" is represented by the inequality x \geq 12. This indicates that x can be 12 or any number larger than 12, making it the correct choice.

• A closed circle on -1 with shading to the right.

• An open circle on -1 with shading to the right.

• A closed circle on -1 with shading to the left.

• An open circle on -1 with shading to the left.

Answer explanation

The inequality x > -1 means x is greater than -1, so we use an open circle at -1 to indicate that -1 is not included. The shading to the right shows all numbers greater than -1.

• 9

• 8

• 7

• 6

Answer explanation

The inequality x ≤ 8 includes all numbers less than or equal to 8. The number 9 is greater than 8, so it does not satisfy the inequality. Therefore, 9 is not part of the solution set.

• Yes, because 3 is less than 4.

• No, because 3 is not less than 4.

• Yes, because 3 is greater than 4.

• No, because 3 is equal to 4.

Answer explanation

Substituting 3 into the inequality x < 4 shows that 3 is indeed less than 4. Therefore, the statement is true, making the correct answer: Yes, because 3 is less than 4.