Equations And Inequalities Quiz Questions And Answers

1. Solve for g:

2g + 1 = 13

G = 6

G = 7

G = 9

G = 5

To solve the equation 2g + 1 = 13, we need to isolate the variable g. First, we subtract 1 from both sides of the equation to get 2g = 12. Then, we divide both sides by 2 to get g = 6. Therefore, the correct answer is g = 6.

Explanation

To solve the equation 2g + 1 = 13, we need to isolate the variable g. First, we subtract 1 from both sides of the equation to get 2g = 12. Then, we divide both sides by 2 to get g = 6. Therefore, the correct answer is g = 6.

2. Solve for y:

y - 5 = 12

Y = 7

Y = -7

Y = 17

Y = -17

By solving the equation y - 5 = 12, we can isolate the variable y. Adding 5 to both sides of the equation, we get y = 17. Therefore, the correct answer is y = 17.

Explanation

By solving the equation y - 5 = 12, we can isolate the variable y. Adding 5 to both sides of the equation, we get y = 17. Therefore, the correct answer is y = 17.

3. Solve for x: -6x = 36

X = 6

X = -6

X = 30

X = 42

The equation -6x = 36 can be solved by dividing both sides of the equation by -6. This gives us x = -6, which is the correct answer.

Explanation

The equation -6x = 36 can be solved by dividing both sides of the equation by -6. This gives us x = -6, which is the correct answer.

4. Solve for k:

-3k - 2 = 10

K = 4

K = -3

K = -4

K = 3

To solve the equation -3k - 2 = 10, we need to isolate the variable k. First, we can add 2 to both sides of the equation to get -3k = 12. Then, divide both sides by -3 to solve for k. This gives us k = -4, which is the correct answer.

Explanation

To solve the equation -3k - 2 = 10, we need to isolate the variable k. First, we can add 2 to both sides of the equation to get -3k = 12. Then, divide both sides by -3 to solve for k. This gives us k = -4, which is the correct answer.

5. Solve this inequality:

7y < 14

Y < -2

Y < 2

Y > 2

Y > -2

The inequality 7y

Explanation

The inequality 7y

6. Evaluate for x = 2 and y = -1:

3x + 2y + x

= 0

= 10

= 6

To evaluate the expression for x = 2 and y = -1, we substitute these values into the given expression: 3(2) + 2(-1) + 2. Simplifying this, we get 6 - 2 + 2 = 6. Therefore, the answer is 6.

Explanation

To evaluate the expression for x = 2 and y = -1, we substitute these values into the given expression: 3(2) + 2(-1) + 2. Simplifying this, we get 6 - 2 + 2 = 6. Therefore, the answer is 6.

7. Write an algebraic expression for:

The product of 6 and y

The correct answer is 6y. This is because the question asks for the product of 6 and y, which can be written as 6y. The other options include unnecessary spaces or extra variables (x) that are not mentioned in the question.

Explanation

The correct answer is 6y. This is because the question asks for the product of 6 and y, which can be written as 6y. The other options include unnecessary spaces or extra variables (x) that are not mentioned in the question.

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8. An inequality means that the variable can only be one number. For example, x can only be 6.

True

False

An inequality does not mean that the variable can only be one number. Instead, it means that the variable can take on a range of values that satisfy the given condition. In the example given, x can be any number less than or equal to 6, not just the number 6 itself. Therefore, the statement is false.

Explanation

An inequality does not mean that the variable can only be one number. Instead, it means that the variable can take on a range of values that satisfy the given condition. In the example given, x can be any number less than or equal to 6, not just the number 6 itself. Therefore, the statement is false.

9. Check all of the "clue words" that mean multiply:

Times

Split equally

Product

Less than

The clue words "times" and "product" both indicate multiplication. "Times" is a common word used to denote multiplication, while "product" refers to the result of multiplying two or more numbers together. Therefore, selecting "times" and "product" as the clue words that mean multiply is correct.

Explanation

The clue words "times" and "product" both indicate multiplication. "Times" is a common word used to denote multiplication, while "product" refers to the result of multiplying two or more numbers together. Therefore, selecting "times" and "product" as the clue words that mean multiply is correct.

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10. Solve for d:

6d - 1 > 17

D > -3

D < 3

D > 3

D < -3

The given inequality is 6d - 1 > 17. To solve for d, we need to isolate the variable. Adding 1 to both sides of the inequality gives us 6d > 18. Dividing both sides by 6, we get d > 3. Therefore, the correct answer is d > 3.

Explanation

The given inequality is 6d - 1 > 17. To solve for d, we need to isolate the variable. Adding 1 to both sides of the inequality gives us 6d > 18. Dividing both sides by 6, we get d > 3. Therefore, the correct answer is d > 3.

11. Solve this inequality:

g - 5 ≤ 2

G ≤ -3

G < -3

G < 7

G ≤ 7

The given inequality is g - 5 ≤ 2. To solve for g, we can add 5 to both sides of the inequality to isolate g. This gives us g ≤ 7, which means that g is less than or equal to 7. Therefore, the correct answer is g ≤ 7.

Explanation

The given inequality is g - 5 ≤ 2. To solve for g, we can add 5 to both sides of the inequality to isolate g. This gives us g ≤ 7, which means that g is less than or equal to 7. Therefore, the correct answer is g ≤ 7.

12. Check all of the answers that are showing inequalities:

X = 1

X < 5

7 > k

-2 ≥ u

8 = w

F ≤ -2

H = -1

The correct answer includes all the options that are showing inequalities. The options "x k", "-2 ≥ u", and "f ≤ -2" all represent inequalities. These options indicate that x is less than 5, 7 is greater than k, -2 is greater than or equal to u, and f is less than or equal to -2. Therefore, these options are the correct answers as they satisfy the condition of showing inequalities.

Explanation

The correct answer includes all the options that are showing inequalities. The options "x k", "-2 ≥ u", and "f ≤ -2" all represent inequalities. These options indicate that x is less than 5, 7 is greater than k, -2 is greater than or equal to u, and f is less than or equal to -2. Therefore, these options are the correct answers as they satisfy the condition of showing inequalities.

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13. Which inequality is represented by this graph:

X < 3

X > 3

X ≥ 3

X ≤ 3

The graph shows a number line with an open circle at 3 and an arrow pointing to the right. This indicates that the values of x are greater than 3. Therefore, the correct inequality represented by the graph is x > 3.

Explanation

The graph shows a number line with an open circle at 3 and an arrow pointing to the right. This indicates that the values of x are greater than 3. Therefore, the correct inequality represented by the graph is x > 3.

14. Which inequality is represented by this graph:

X ≤ -2

X < -2

X ≥ -2

X > -2

The graph shows a solid line with a closed dot on -2 on the number line. This indicates that the value of x can equal -2 or any number less than -2. Therefore, the correct inequality that represents the graph is x ≤ -2.

Explanation

The graph shows a solid line with a closed dot on -2 on the number line. This indicates that the value of x can equal -2 or any number less than -2. Therefore, the correct inequality that represents the graph is x ≤ -2.

15. Solve for x:

-2x + 6 ≤ 20

X ≥ -7

X ≥ 7

X ≤ -7

X ≤ 7

The given inequality is -2x + 6 ≤ 20. To solve for x, we need to isolate the variable on one side of the inequality. Subtracting 6 from both sides, we get -2x ≤ 14. Dividing both sides by -2, we have x ≥ -7. Therefore, the correct answer is x ≥ -7.

Explanation

The given inequality is -2x + 6 ≤ 20. To solve for x, we need to isolate the variable on one side of the inequality. Subtracting 6 from both sides, we get -2x ≤ 14. Dividing both sides by -2, we have x ≥ -7. Therefore, the correct answer is x ≥ -7.