One-quarter of the difference of a number and 3 is 2. Find the number.(1 point)
Responses
3 1/2
5/4
20
11
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.
Solve 2/3(x −6)=1/4
(1 point)
Responses
−27
15
−15
27
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.
To find the number, we need to solve the equation that is given.
The equation states that one-quarter of the difference of a number and 3 is equal to 2.
Let's break down the information given:
Let x be the unknown number.
The difference between the number and 3 is x - 3.
One-quarter of that difference is (1/4)(x - 3).
According to the equation, this is equal to 2:
(1/4)(x - 3) = 2
To find the value of x, we can solve this equation.
First, let's remove the fraction by multiplying both sides of the equation by 4:
4 * (1/4)(x - 3) = 4 * 2
Simplifying:
x - 3 = 8
Next, let's isolate x by adding 3 to both sides of the equation:
x - 3 + 3 = 8 + 3
Simplifying:
x = 11
Therefore, the number is 11.