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

Question

Responses

3 1/2

5/4

20

11

Answer 1

To solve this problem, let's represent the unknown number with the variable "x".

The difference between the number and 3 is given by "x - 3".

One-quarter of this difference is expressed as (1/4)(x - 3).

According to the problem, this expression is equal to 2.

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

Now, let's solve the equation for x.

Multiply both sides of the equation by 4 to get rid of the fraction:

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

Simplifying the equation:

(x - 3) = 8

Add 3 to both sides of the equation:

x - 3 + 3 = 8 + 3

Simplifying again:

x = 11

Therefore, the number is 11.

The correct answer is 11.

Answer 2

Solve 2/3(x −6)=1/4
(1 point)
Responses

−27

15

−15

27

Answer 3

To solve the equation 2/3(x - 6) = 1/4, you need to follow these steps:

1. Distribute the 2/3 to the terms inside the parentheses:
(2/3)(x) - (2/3)(6) = 1/4

2. Simplify by multiplying:
(2x/3) - 12/3 = 1/4

3. Simplify the fractions:
(2x/3) - 4 = 1/4

4. Convert 1/4 to a common denominator with 3:
(2x/3) - 4 = 3/12

5. Multiply both sides of the equation by 12 to eliminate the fraction:
12 * (2x/3) - 12 * 4 = 12 * (3/12)

6. Simplify and solve for x:
8x - 48 = 3

7. Add 48 to both sides of the equation:
8x - 48 + 48 = 3 + 48
8x = 51

8. Divide both sides by 8 to solve for x:
8x/8 = 51/8
x = 6.375

Therefore, the solution to the equation is x = 6.375.

The correct answer is 6.375.