A number minus 5 times
It’s reciprocal is 7
Let's solve the equation step by step.
Let's assume the number is "x".
According to the given information, we have the equation:
x - 5 * (1/x) = 7
To solve this equation, let's simplify it.
First, let's simplify 5 * (1/x):
5 * (1/x) can be written as 5/x.
Now let's substitute this simplified expression back into the equation:
x - 5/x = 7
To eliminate the fraction, let's multiply the entire equation by x:
x^2 - 5 = 7x
Next, let's bring all terms to one side of the equation:
x^2 - 7x - 5 = 0
Now, we have a quadratic equation. Let's solve it using the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = -7, and c = -5.
Applying the quadratic formula, we get:
x = (-(-7) ± √((-7)^2 - 4 * 1 * -5)) / (2 * 1)
Simplifying:
x = (7 ± √(49 + 20)) / 2
x = (7 ± √69) / 2
Therefore, the solutions to the equation are:
x = (7 + √69) / 2
x = (7 - √69) / 2
These are the possible values for the number that satisfies the given conditions.
To solve this problem, we can set up an equation. Let's first assign a variable to the number, say "x".
The phrase "a number minus 5" can be written as "x - 5".
The phrase "it's reciprocal is 7" means that the reciprocal of the number, which is 1 divided by the number, is equal to 7. So, we can write this as:
1/x = 7
Now, we can set up the equation:
x - 5 = 1/7
To find the value of x, we need to isolate it on one side of the equation. We can start by adding 5 to both sides of the equation:
x - 5 + 5 = 1/7 + 5
This simplifies to:
x = 1/7 + 5
To add the fractions, we need a common denominator. The common denominator of 7 and 1 is 7. So, we can write:
x = 1/7 + 35/7
Combining the fractions, we get:
x = 36/7
Therefore, the value of x is 36/7.
i want to be helping me to answer the math
A number ... x
Its reciprocal ... 1/x
5 times its reciprocal ... 5/x
is ... =
so now just make the equation