Solving Inequalities and satisfied Regions Quiz

• A closed circle at 3 with a line extending to the right

• An open circle at 3 with a line extending to the left

• A closed circle at 3 with a line extending to the left

• An open circle at 3 with a line extending to the right

Answer explanation

The correct choice is a closed circle at 3 with a line extending to the left, indicating x is less than or equal to 3. This shows all values less than or equal to 3 are included in the solution set.

Answer explanation

To solve the inequality 5x > 20, divide both sides by 5 to get x > 4. Therefore, the correct answer is x > 4.

• Yes

• No

Answer explanation

Substitute x = -1 into the inequality: 3(-1) + 2 ≤ 5. Simplify to -3 + 2 ≤ 5, which becomes -1 ≤ 5. Since -1 is less than or equal to 5, the statement is true. Therefore, the value x = -1 satisfies the inequality.

Answer explanation

The correct choice is a dashed line for y = 2x - 1 with shading above the line, representing the inequality y > 2x - 1.

Answer explanation

To solve the inequality -3x + 4 ≥ 1, first subtract 4 from both sides to get -3x ≥ -3. Then divide by -3, remembering to flip the inequality sign, to get x ≤ -1. Therefore, the correct answer is x ≤ -1.

• Yes

• No

Answer explanation

Substitute x=3 into the inequality: 2(3) - 5 < 1. Simplify to get 6 - 5 < 1, which is 1 < 1. Since this is false, the answer is No.

Answer explanation

To solve the inequality -2x + 7 < 3, first subtract 7 from both sides to get -2x < -4. Then, divide by -2 (which reverses the inequality) to find x > 2.

Answer explanation

To solve the inequality 4x - 5 ≤ 3, add 5 to both sides to get 4x ≤ 8. Then, divide by 4 to find x ≤ 2. Therefore, the correct answer is x ≤ 2.