3.1-3.3 Multi-Step Inequalities Practice

Solve the inequality: 3x + 5 > 17

To solve this inequality, first subtract 5 from both sides to get 3x > 12. Then, divide both sides by 3 to find x > 4. Therefore, the solution to the inequality is all values of x greater than 4.

• x = 4

• x > 4

• x > 17

• x < 4

Answer explanation

To solve the inequality 3x + 5 > 17, subtract 5 from both sides to get 3x > 12. Then, divide by 3 to find x > 4. Thus, the correct answer is x > 4.

Tags

CCSS.7.EE.B.4B

Solve the inequality: 4a + 7 ≥ 31

Detailed Explanation:
To solve the inequality 4a + 7 ≥ 31, follow these steps:
1. Subtract 7 from both sides to isolate the term with 'a':
  4a + 7 - 7 ≥ 31 - 7
  4a ≥ 24
2. Divide both sides by 4 to solve for 'a':
  4a / 4 ≥ 24 / 4
  a ≥ 6
So, the solution to the inequality is a ≥ 6.

• a > 6

• a ≤ 6

• a ≥ 6

• a = 6

Answer explanation

To solve the inequality 4a + 7 ≥ 31, subtract 7 from both sides to get 4a ≥ 24. Then, divide by 4 to find a ≥ 6. Thus, the correct answer is a ≥ 6.

Tags

CCSS.7.EE.B.4B

Graph the inequality on a number line: y < -3

Explanation: To graph the inequality y < -3 on a number line, you need to show all values less than -3. Since the inequality is strictly less than (not less than or equal to), you use an open circle at -3 to indicate that -3 is not included. Then, shade the number line to the left of -3 to represent all values less than -3.

• Draw a closed circle at -3 and shade to the right.

• Draw an open circle at -3 and shade to the left.

• Draw an open circle at -3 and shade to the right.

• Draw a closed circle at -3 and shade to the left.

Answer explanation

The inequality y < -3 means y is less than -3. We use an open circle at -3 to indicate that -3 is not included, and shade to the left to show all values less than -3.

Tags

CCSS.6.EE.B.8

Graph the inequality on a number line: a ≥ 2

Explanation: The inequality a ≥ 2 means that a can be any value greater than or equal to 2. On a number line, this is represented by a closed circle at 2 (showing that 2 is included) and shading to the right to indicate all numbers greater than 2 are included.

• Open circle at 2, shade to the left

• Closed circle at 2, shade to the left

• Closed circle at 2, shade to the right

• Open circle at 2, shade to the right

Answer explanation

The inequality a ≥ 2 means a can be 2 or any number greater than 2. We use a closed circle at 2 to indicate that 2 is included, and shade to the right to show all values greater than 2.

Tags

CCSS.6.EE.B.8

Graph the inequality on a number line: b ≤ 5

Explanation: The inequality b ≤ 5 means that b can be any value less than or equal to 5. On a number line, this is represented by drawing a closed circle at 5 (to show that 5 is included) and shading all numbers to the left of 5 (to show all values less than 5 are included).

• Draw a closed circle at 5 and shade to the left.

• Draw a closed circle at 5 and shade to the left and right.

• Draw an open circle at 5 and shade to the right.

• Draw a closed circle at 5 and shade to the right.

Answer explanation

The inequality b ≤ 5 means b can be 5 or any number less than 5. A closed circle at 5 indicates that 5 is included, and shading to the left shows all numbers less than 5 are also included.

Tags

CCSS.6.EE.B.8

Solve the inequality: 2c + 9 < 25

Explanation:
To solve the inequality, first subtract 9 from both sides:
2c + 9 - 9 < 25 - 9
2c < 16
Now, divide both sides by 2:
2c/2 < 16/2
c < 8
So, the solution to the inequality is c < 8.

• c < 8

• c = 8

• c > 8

• c < 5

Answer explanation

To solve the inequality 2c + 9 < 25, subtract 9 from both sides to get 2c < 16. Then, divide by 2 to find c < 8. Thus, the correct answer is c < 8.

Tags

CCSS.7.EE.B.4B

Solve the inequality: 3d - 6 ≥ 15

Explanation:
To solve the inequality, start by isolating the variable d.
Step 1: Add 6 to both sides:
3d - 6 + 6 ≥ 15 + 6
3d ≥ 21
Step 2: Divide both sides by 3:
3d / 3 ≥ 21 / 3
d ≥ 7
So, the solution to the inequality is d ≥ 7.

• d ≥ 7

• d = 7

• d > 10

• d ≤ 7

Answer explanation

To solve the inequality 3d - 6 ≥ 15, add 6 to both sides to get 3d ≥ 21. Then, divide by 3 to find d ≥ 7. Thus, the correct answer is d ≥ 7.

Tags

CCSS.7.EE.B.4B

Which inequality is represented by the following graph:

Notice that the graph shows an open circle at -8 and the arrow extends to the right, indicating all values greater than -8 but not including -8 itself. An open circle means that the endpoint is not included in the solution set.

Based on this, which of the following inequalities matches the graph?

• x < -8

• x > -8

• x ≥ -8

• x ≤ -8

Answer explanation

The graph shows an open circle at -8, indicating that -8 is not included, and shading to the right, which means x is greater than -8. Therefore, the correct inequality is x > -8.

Tags

CCSS.6.EE.B.8

Which inequality is represented by the following graph?

Observe the number line: The graph shows a closed circle at 9 and a shaded line extending to the right. A closed circle means that 9 is included in the solution, and the shading to the right means all numbers greater than 9 are included. Therefore, the inequality represented is:

• x > 9

• x < 9

• x ≥ 9

• x ≤ 9

Answer explanation

The graph shows a closed circle at 9, indicating that 9 is included in the solution. The shading extends to the right, meaning all values greater than or equal to 9 satisfy the inequality. Thus, the correct choice is x ≥ 9.

Tags

CCSS.6.EE.B.8

Write the word sentence as an inequality
a number b is at least -16

Explanation:
When we say that a number b is at least -16, it means that b can be -16 or any number greater than -16. In mathematical terms, this is represented by the inequality b ≥ -16. The symbol '≥' means 'greater than or equal to'.

• b ≥ -16

• b ≤ -16

• b = -16

• b > -16

Answer explanation

The phrase 'at least -16' means that b can be -16 or any number greater than -16. This is represented by the inequality b ≥ -16, making it the correct choice. The other options do not accurately reflect this condition.

Tags

CCSS.6.EE.B.8