7th Inequalities Review

• A closed circle on 3 with shading to the right

• An open circle on 3 with shading to the right

• A closed circle on 3 with shading to the left

• An open circle on 3 with shading to the left

Answer explanation

The inequality x > 3 means x is greater than 3, so we use an open circle at 3 to indicate that 3 is not included. The shading to the right shows all numbers greater than 3.

Write an inequality for the following word problem: "A number decreased by 5 is less than 12."

Answer explanation

The phrase 'A number decreased by 5' translates to 'x - 5'. The statement 'is less than 12' indicates the inequality should be '< 12'. Therefore, the correct inequality is x - 5 < 12.

Answer explanation

To solve the inequality x + 7 ≤ 10, subtract 7 from both sides: x ≤ 3. Thus, the correct answer is x ≤ 3.

Answer explanation

To solve the inequality 3x - 4 > 5, first add 4 to both sides: 3x > 9. Then, divide by 3: x > 3. Thus, the correct answer is x > 3.

• You must be exactly 8 years old to ride.

• You must be younger than 8 years old to ride.

• You must be 8 years old or older to ride.

• You cannot ride if you are 8 years old.

Answer explanation

The inequality x ≥ 8 means that you can be 8 years old or older to ride the roller coaster. Therefore, the correct interpretation is that you must be 8 years old or older to ride.

• A closed circle on -2 with shading to the left

• An open circle on -2 with shading to the left

• A closed circle on -2 with shading to the right

• An open circle on -2 with shading to the right

Answer explanation

The inequality x ≤ -2 means x can be -2 or any number less than -2. We represent -2 with a closed circle to indicate it is included, and shade to the left to show all values less than -2.

Write an inequality for the following word problem: "The sum of a number and 4 is at least 10."

Answer explanation

The phrase 'at least' indicates a greater than or equal to relationship. Therefore, the sum of a number (x) and 4 must be greater than or equal to 10, leading to the inequality x + 4 ≥ 10.

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 answer is x < 4.

Answer explanation

To solve the inequality 5x + 2 ≤ 17, subtract 2 from both sides to get 5x ≤ 15. Then, divide by 5 to find x ≤ 3. Thus, the correct answer is x ≤ 3.

• You must be exactly 15 years old to enter.

• You must be younger than 15 years old to enter.

• You must be 15 years old or older to enter.

• You cannot enter if you are younger than 15 years old.

Answer explanation

The inequality x < 15 means that to enter the junior competition, you must be younger than 15 years old. Therefore, the correct interpretation is that you must be younger than 15 years old to enter.