Question

One-quarter of the difference of a number and 3 is 2. Find the number.(1 point)
Responses

54
5 fourths

20
20

312
3 and 1 half

11

Answer 1

proof

Answer 2

Solve 23(x −6)=14 (1 point)
Responses

−27
negative 27

−15
negative 15

15
15

27
27

Answer 3

Solve 2/3(x −6)=14 (1 point)
Responses

−27
negative 27

−15
negative 15

15
15

27
27

Answer 4

olve 23(x −6)=14 (1 point)
Responses

−27
negative 27

−15
negative 15

15
15

27

Answer 5

−27
negative 27

−15
negative 15

15
15

27

Answer 6

11

Answer 7

To prove that the number is 11, we can use algebraic equations.

Let's assume the number is x.

According to the given information, "One-quarter of the difference of a number and 3 is 2," we can write the equation as:

(1/4)(x - 3) = 2

To solve for x, we can first distribute the 1/4 to the terms inside the parentheses:

(x/4) - (3/4) = 2

Next, we can add (3/4) to both sides of the equation to isolate x:

(x/4) = 2 + (3/4)

Combining the terms on the right side:

(x/4) = 8/4 + 3/4

(x/4) = 11/4

Now, to solve for x, we can multiply both sides by 4:

4(x/4) = 4(11/4)

x = 44/4

Simplifying:

x = 11

Therefore, the number is 11.

Answer 8

To solve the equation 23(x - 6) = 14, we can use algebraic steps.

First, distribute the 23 to the terms inside the parentheses:

23x - 138 = 14

Next, isolate the term with the variable by adding 138 to both sides of the equation:

23x = 14 + 138

Combine the terms on the right side:

23x = 152

Finally, solve for x by dividing both sides of the equation by 23:

x = 152/23

Simplifying the fraction, we get:

x ≈ 6.61

Therefore, the solution to the equation is approximately 6.61.

Answer 9

To solve the equation (2/3)(x - 6) = 14, we can use algebraic steps.

First, distribute the 2/3 to the terms inside the parentheses:

(2/3)x - 12/3 = 14

Simplify the equation:

(2/3)x - 4 = 14

Next, isolate the term with the variable by adding 4 to both sides of the equation:

(2/3)x = 14 + 4

Combine the terms on the right side:

(2/3)x = 18

Finally, solve for x by multiplying both sides of the equation by 3/2:

(3/2)(2/3)x = (3/2)(18)

Simplifying:

x = 27/2

Therefore, the solution to the equation is 27/2, which can also be written as 13.5.

Answer 10

To solve the equation 23(x - 6) = 14, we can use algebraic steps.

First, distribute the 23 to the terms inside the parentheses:

23x - 138 = 14

Next, isolate the term with the variable by adding 138 to both sides of the equation:

23x = 14 + 138

Combine the terms on the right side:

23x = 152

Finally, solve for x by dividing both sides of the equation by 23:

x = 152/23

Simplifying the fraction, we get:

x ≈ 6.61

Therefore, the solution to the equation is approximately 6.61.

Answer 11

I apologize for the confusion, but none of the given options is the correct solution to the equation 23(x - 6) = 14.

To solve the equation, let's go step-by-step:

First, distribute the 23 to the terms inside the parentheses:

23x - 138 = 14

Next, isolate the term with the variable by adding 138 to both sides of the equation:

23x = 14 + 138 = 152

Finally, solve for x by dividing both sides of the equation by 23:

x = 152/23 ≈ 6.61

So, the correct solution to the equation is approximately 6.61, not any of the options provided.