Half the sum of a certain number and 7 is equal to one quarter of the difference of the number from 3 find the number
Let's call the certain number "x".
According to the problem:
(1/2)(x + 7) = (1/4)(3 - x)
To solve for x, we can first simplify the equation by getting rid of the fractions:
2(x + 7) = 4(3 - x)
Then distribute on both sides:
2x + 14 = 12 - 4x
Combine like terms:
2x + 4x = 12 - 14
6x = -2
Divide both sides by 6:
x = -2/6
Simplifying further:
x = -1/3
Therefore, the certain number is -1/3.
Let's denote the certain number as "x".
According to the given information, half the sum of the certain number and 7 is equal to one quarter of the difference of the number from 3.
Mathematically, this can be written as:
(1/2)(x + 7) = (1/4)(3 - x)
To solve for x, we can simplify the equation step by step:
1. Distribute the 1/2 on the left side:
(1/2)x + (1/2)(7) = (1/4)(3 - x)
2. Simplify the left side:
(1/2)x + 7/2 = (1/4)(3 - x)
3. Distribute the 1/4 on the right side:
(1/2)x + 7/2 = (1/4)(3) - (1/4)x
4. Simplify the right side:
(1/2)x + 7/2 = 3/4 - (1/4)x
5. Move the terms with x to one side:
(1/2)x + (1/4)x = 3/4 - 7/2
6. Find a common denominator for the fractions on the right side:
(1/2)x + (1/4)x = 6/8 - 28/8
7. Combine like terms on the right side:
(1/2)x + (1/4)x = -22/8
8. Find a common denominator for the fractions on the left side:
(2/4)x + (1/4)x = -22/8
9. Combine like terms on the left side:
(3/4)x = -22/8
10. Simplify the right side:
(3/4)x = -11/4
11. Multiply both sides by the reciprocal of 3/4, which is 4/3:
x = (-11/4)(4/3)
12. Simplify the right side:
x = -44/12
13. Reduce the fraction:
x = -11/3
Therefore, the certain number is -11/3.
To find the number, let's assign a variable to it. Let's call the number "x".
According to the problem, "Half the sum of a certain number and 7 is equal to one quarter of the difference of the number from 3." This can be written as the following equation:
(1/2)(x + 7) = (1/4)(3 - x)
To solve for x, we can simplify the equation step by step:
First, let's simplify both sides of the equation by multiplying them by their respective denominators:
2 * (1/2)(x + 7) = 4 * (1/4)(3 - x)
This simplifies to:
x + 7 = 3 - x
Next, let's isolate the variable x by moving the x term to the left side of the equation and the constant term to the right side:
x + x = 3 - 7
This simplifies to:
2x = -4
Next, let's solve for x by dividing both sides of the equation by 2:
x = -4 / 2
This simplifies to:
x = -2
Therefore, the number we are looking for is -2.