Question 55488: PLEASE HELP ME:
Solve the equation 4^2x+1=2^3x+6
Found 2 solutions by funmath, Genius:
Answer by funmath(2933)   (Show Source):
Answer by Genius(17) (Show Source):
You can put this solution on YOUR website! First, let's work on the left hand side of your equation, the 4^2x+1
This means, for instance, to see if it can be simplified at all.
16
Multiply x and 16
Multiply x and 1
The x just gets copied along.
x
x
16x
16x+1
So, all-in-all, the left hand side of your equation can be written as: 16x+1
--------------------------------------------------------------------------------
Now, let's work on the right hand side of your equation, the 2^3x+6
8
Multiply x and 8
Multiply x and 1
The x just gets copied along.
x
x
8x
8x+6
The right hand side of your equation can be written as: 8x+6
--------------------------------------------------------------------------------
So with these (any) simplifications, the equation we'll set out to solve is:
16x+1 = 8x+6
Move the 1 to the right hand side by subtracting 1 from both sides, like this:
From the left hand side:
1 - 1 = 0
16x
From the right hand side:
6 - 1 = 5
5+8x
Now, the equation reads:
16x = 5+8x
Move the 8x to the left hand side by subtracting 8x from both sides, like this:
From the left hand side:
16x - 8x = 8x
8x
From the right hand side:
8x - 8x = 0
5
Now, the equation reads:
8x = 5
To isolate the x, we have to divide both sides of the equation by the other variables
around the x on the left side of the equation.
--------------------------------------------------------------------------------
The last step is to divide both sides of the equation by 8 like this:
To divide x by 1
The x just gets copied along in the numerator.
x
8x ÷ 8 = x
5 ÷ 8 = 5/8 or 0.625
The solution to your equation is:
x = 5/8 or 0.625
|
|
|
