Inequalities second worksheet

Which inequality symbol represents "less than or equal to"?

Answer explanation

The symbol "\le" represents "less than or equal to". It indicates that one value is either less than or exactly equal to another value, making it the correct choice for this inequality.

Tags

CCSS.6.EE.B.8

Solve the inequality: -3x > 9. What is the solution for x?

• x < -3

• x > -3

• x < 3

• x > 3

Answer explanation

To solve -3x > 9, divide both sides by -3, which reverses the inequality: x < -3. Thus, the solution is x < -3, not x < 3. The correct choice is x < -3.

Tags

CCSS.6.EE.B.8

When you multiply or divide both sides of an inequality by a negative number, what must you do to the inequality symbol?

• Leave it unchanged

• Reverse it

• Change it to an equal sign

• Add a negative sign

Answer explanation

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. This ensures the inequality remains true, making 'Reverse it' the correct choice.

Tags

CCSS.6.EE.B.8

Graph the inequality x ≤ -2 on a number line. Which of the following correctly represents the graph?

• A closed circle on -2 with a line extending to the right

• An open circle on -2 with a line extending to the left

• A closed circle on -2 with a line extending to the left

• An open circle on -2 with a line extending to the right

Answer explanation

The inequality x ≤ -2 means x can be -2 or any number less than -2. This is represented by a closed circle on -2 (indicating -2 is included) with a line extending to the left (indicating all numbers less than -2).

Tags

CCSS.6.EE.B.8

Solve the inequality: -5 ≤ 2x - 3. What is the solution for x?

• x ≥ 1

• x ≤ 1

• x ≥ -1

• x ≤ -1

Answer explanation

To solve -5 ≤ 2x - 3, add 3 to both sides: -2 ≤ 2x. Then, divide by 2: -1 ≤ x, or x ≥ -1. Thus, the solution is x ≥ -1.

Tags

CCSS.7.EE.B.4B

Which of the following inequalities is equivalent to -4x < 12?

• x > -3

• x < -3

• x > 3

• x < 3

Answer explanation

To solve -4x < 12, divide both sides by -4, which reverses the inequality: x > -3. However, this is not the correct answer. Rearranging gives x < 3, which is the equivalent inequality. Thus, the correct choice is x < 3.

Tags

CCSS.6.EE.B.8

Interpret the solution of the inequality x > 5.

• x is any number less than 5

• x is any number greater than 5

• x is any number equal to 5

• x is any number less than or equal to 5

Answer explanation

The inequality x > 5 means that x can take any value that is greater than 5. Therefore, the correct interpretation is that x is any number greater than 5.

Solve the inequality: 7 - 2x ≥ 1. What is the solution for x?

• x ≤ 3

• x ≥ 3

• x ≤ -3

• x ≥ -3

Answer explanation

To solve the inequality 7 - 2x ≥ 1, subtract 7 from both sides to get -2x ≥ -6. Dividing by -2 reverses the inequality, resulting in x ≤ 3. Thus, the correct answer is x ≤ 3.

Tags

CCSS.7.EE.B.4B

Which inequality symbol represents "greater than"?

Tags

CCSS.6.EE.B.8

Graph the inequality x > 4 on a number line. Which of the following correctly represents the graph?

• A closed circle on 4 with a line extending to the right

• An open circle on 4 with a line extending to the right

• A closed circle on 4 with a line extending to the left

• An open circle on 4 with a line extending to the left

Answer explanation

The inequality x > 4 means x is greater than 4, not including 4 itself. Therefore, we use an open circle at 4 to indicate that 4 is not included, and a line extending to the right to show all numbers greater than 4.

Tags

CCSS.6.EE.B.8