Solving and Graphing Inequalities

Identify the solution set of the inequality: x < 5

• x > 5

• x = 5

• x < 5

• x ≤ 5

Answer explanation

The solution set of the inequality x < 5 is x values that are less than 5. Therefore, the correct choice is x < 5.

Graph the inequality -3x ≥ 9 on a number line

• x < -3

• x ≤ -3

• x = -3

• x > 3

Answer explanation

The correct choice is x ≤ -3 because the inequality -3x ≥ 9 represents all values of x that are less than or equal to -3.

Solve the inequality 2x + 4 > 10

• x > 10

• x > 3

• x = 3

• x < 3

Answer explanation

To solve the inequality 2x + 4 > 10, subtract 4 from both sides to get 2x > 6. Then divide both sides by 2 to find x > 3. Therefore, the correct choice is x > 3.

Explain the concept of open and closed circles on number lines in the context of inequalities

• Open circles indicate values that are not included in the solution set, while closed circles indicate values that are included in the solution set.

• Open circles indicate values that are included in the solution set, while closed circles indicate values that are not included in the solution set.

• Open circles indicate values that are included in the solution set, while closed circles indicate values that are also not included in the solution set.

• Open circles indicate values that are not included in the solution set, while closed circles indicate values that are also not included in the solution set.

Answer explanation

Open circles indicate values not in solution set, closed circles indicate values in solution set.

Solve the inequality 3(x - 2) ≤ 9

• x ≥ 5

• x = 2

• x < 5

• x ≤ 5

Answer explanation

To solve the inequality 3(x - 2) ≤ 9, we first distribute the 3, giving us 3x - 6 ≤ 9. Then, we add 6 to both sides to isolate the variable, resulting in 3x ≤ 15. Finally, we divide both sides by 3 to solve for x, giving us x ≤ 5. Therefore, the correct choice is x ≤ 5.

Identify the solution set of the inequality: y ≥ -2

• y > -2

• y < -2

• y = -2

• y ≥ -2

Answer explanation

The solution set of the inequality is y greater than or equal to -2, as indicated by the correct choice 'y ≥ -2'.

Graph the inequality 4 + 2y < 10 on a number line

• y < 2

• y < 3

• y = 3

• y > 3

Answer explanation

The correct choice is 'y < 3' because it represents all values of y that make the inequality 4 + 2y < 10 true.

Solve the inequality 5 - 2x < 13

• x < -4

• x = 5

• x > 10

• x > -4

Answer explanation

To solve the inequality 5 - 2x < 13, we subtract 5 from both sides to get -2x < 8. Dividing both sides by -2, we find x > -4. Therefore, the correct choice is x > -4.

Explain the difference between solving one-step and multi-step inequalities

• One-step inequalities involve solving for one variable, while multi-step inequalities involve solving for multiple variables.

• One-step inequalities are solved using only addition, while multi-step inequalities use only subtraction.

• One-step inequalities always have a solution, while multi-step inequalities may not have a solution.

• One-step inequalities are solved using only one operation, while multi-step inequalities require multiple operations to solve.

Answer explanation

One-step inequalities involve solving for one variable, while multi-step inequalities involve solving for multiple variables.

Graph the inequality 2x + 3 ≤ 7 on a number line

• x > 2

• x ≤ 2

• x = 2

• x < 2

Answer explanation

The correct choice is x ≤ 2 because the inequality 2x + 3 ≤ 7 represents all values of x that are less than or equal to 2. Graphing this inequality on a number line shows that x can take any value less than or equal to 2.