Sentence. . If two times the reciprocal of a number is subtracted from 3 times the number, the difference is 1. Find the number. (4 points)

Question

asked Sep 25, 2024 13.4k views

1 Answer

Uli Gerhardt · Answer 1 · 2024-10-01T06:38:29+0000

To find the number, we set up an equation using the given information and solve for x. The possible values for the number are 1 or -2/3.

Let's represent the number as x.

According to the given information, we can write the equation as: 3x - (2/x) = 1.

To solve for x, we need to eliminate the fraction. We can do this by multiplying all terms by x:

3x^2 - 2 = x.

Now, rearrange the equation and solve for x:

3x^2 - x - 2 = 0.

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, where a = 3, b = -1, c = -2, we can find the values of x as x = 1 or x = -2/3.

Therefore, the possible values for the number are 1 or -2/3.