Solve the following equations for x:
X = 2 + (1/x) , X = 3 + (1/x)
How do I do this type of problem? Thanks
X = 2 + (1/x)
Multiply both sides by x
Xx = 2x + 1
Divide both sides by X
x = (2x + 1)/X
Now, you do the other problem.
It's done the same way.
Oh so there's no number, because I got that originally, but I didn't get a specific number. I tried using the quadratic equation so x equaled 2 and -1, but when plugged in neither worked.
To solve the given equations for x, we need to find a value of x that satisfies both equations simultaneously. Let's solve them step by step:
1. Start with the first equation: X = 2 + (1/x)
Step 1: Multiply both sides of the equation by x to eliminate the fraction:
X * x = 2x + 1
Step 2: Simplify the equation by distributing X to both terms on the right side:
X * x = 2x + 1
Xx = 2x + 1
Step 3: Move all terms to one side of the equation by subtracting 2x and 1 from both sides:
Xx - 2x - 1 = 0
Step 4: Combine like terms:
(X - 2)x - 1 = 0
Step 5: Simplify further if possible:
Xx - 2x - 1 = 0
Step 6: Now let's move on to the second equation: X = 3 + (1/x)
Step 7: Repeat the same steps as above, multiplying both sides by x and rearranging the equation:
X * x = 3x + 1
Xx = 3x + 1
Xx - 3x - 1 = 0
2. Now we have two equations:
(X - 2)x - 1 = 0
Xx - 3x - 1 = 0
Since we know that both equations are true simultaneously, we can set them equal to each other:
(X - 2)x - 1 = Xx - 3x - 1
Step 8: Distribute X to terms on the right side:
(X - 2)x - 1 = Xx - 3x - 1
Xx - 2x - 1 = Xx - 3x - 1
Step 9: Subtract Xx from both sides to eliminate the X variable:
Xx - Xx - 2x - 1 = Xx - Xx - 3x - 1
-2x - 1 = -3x - 1
Step 10: Add 3x to both sides to isolate the variable term:
-2x - 1 + 3x = -3x - 1 + 3x
x - 1 = -1
Step 11: Add 1 to both sides:
x - 1 + 1 = -1 + 1
x = 0
3. Therefore, the solution to the given equations is x = 0.
By following these steps, you can solve similar problems where you have multiple equations.