Solving Inequalities Quiz

Solving one-step inequality: Solve for x: 2x + 5 < 11

• x > 3

• x < 5

• x < 3

• x = 3

Answer explanation

To solve the inequality 2x + 5 < 11, subtract 5 from both sides to get 2x < 6. Then divide both sides by 2 to find x < 3. Therefore, the correct choice is x < 3.

Solving one-step inequality: Solve for y: 3y - 7 > 14

• y > 7

• y < 7

• y + 7 > 14

• y = 7

Answer explanation

To solve the inequality 3y - 7 > 14, we add 7 to both sides to isolate the variable. This gives us 3y > 21. Dividing both sides by 3, we find y > 7. Therefore, the correct choice is y > 7.

Solving one-step inequality: Solve for z: 4z/2 >= 6

• z <= 3

• z > 3

• z = 3

• z >= 3

Answer explanation

To solve the inequality, divide both sides by 2. The inequality becomes 2z >= 6. Divide both sides by 2 again to get z >= 3. Therefore, the correct choice is z >= 3.

Solving one-step inequality: Solve for a: 5a - 3 <= 12

• a <= 3

• a < 3

• a = 15

• a >= 3

Answer explanation

To solve the inequality, add 3 to both sides: 5a <= 15. Divide both sides by 5: a <= 3. Therefore, the correct choice is a <= 3.

Solving one-step inequality: Solve for b: 2b + 8 > 20

• b < 6

• b = 6

• b > 20

• b > 6

Answer explanation

To solve the inequality 2b + 8 > 20, subtract 8 from both sides to get 2b > 12. Then divide both sides by 2 to find b > 6. Therefore, the correct choice is b > 6.

Graphing inequality on a number line: Graph the inequality: x < 3

• Open circle at 3 and shade to the right

• Open circle at 3 and shade to the left

• Closed circle at 3 and shade to the left

• Open circle at 3 and shade to the right

Answer explanation

The correct choice is 'Open circle at 3 and shade to the left' because the inequality x < 3 represents all values less than 3, excluding 3 itself.

Graphing inequality on a number line: Graph the inequality: y >= -2

• Draw a solid line at y = -2 and shade the area above the line

• Draw a solid line at y = -2 and shade the area below the line

• Draw a solid line at y = 2 and shade the area below the line

• Draw a dashed line at y = -2 and shade the area above the line

Answer explanation

To graph the inequality y >= -2, draw a solid line at y = -2 and shade the area above the line.

Graphing inequality on a number line: Graph the inequality: z < 5

• Open circle at 5, shade to the right

• Open circle at 5, shade to the left

• Closed circle at 5, shade to the left

• Open circle at 5, shade to the right and left

Answer explanation

The correct choice is 'Open circle at 5, shade to the left' because the inequality is z < 5, which means z is less than 5 and does not include 5 itself.

Graphing inequality on a number line: Graph the inequality: a > 1

• Graph an open circle at 1 and shade the area to the left and right of 1.

• Graph a closed circle at 1 and shade the area to the right of 1.

• Graph an open circle at 1 and shade the area to the left of 1.

• Graph an open circle at 1 and shade the area to the right of 1.

Answer explanation

Graph an open circle at 1 and shade the area to the right of 1. This choice correctly represents the inequality a > 1.

Graphing inequality on a number line: Graph the inequality: b <= 4

• Draw a closed circle at 4 and shade to the right.

• Draw a closed circle at 4 and shade to the left.

• Draw an open circle at 4 and shade to the left.

• Draw a closed circle at 4 and shade to the right and left.

Answer explanation

To graph the inequality b <= 4, draw a closed circle at 4 and shade to the left. This represents all values of b that are less than or equal to 4.