Answer: x = 3
Step-by-step explanation: To solve for <em>x</em> in the equation you see here, our goal is to get <em>x</em> by itself.
Our first step will be to isolate the term containing <em>x</em> which in this case is 2x. To isolate 2x, we have to get rid of this +3 by subtracting from both sides of the equation.
On the left, +3 -3 cancels and we're left with 2x. On the right, 9 - 3 simplifies to 6.
So now we have the equation 2x = 6.
To get <em>x</em> by itself since it's being multiplied by 2, we just to divide by 2 on both sides of the equation. On the left, the 2's cancel and we're left with <em>x</em>. On the right, 
simplifies to 3 so our answer is <em>x = 3</em>.
Answer:
4 red marbles
Step-by-step explanation:
green marbles = 9r
red marbles = r
9r + r = 40
10r = 40
r = 4 = red marbles
Answer:
- x = 4
- length = 19 ft
- width = 11 ft
Step-by-step explanation:
The area is given by the product of length and width.
A = LW
209 = (4x +3)(4x -5)
209 = 16x^2 -8x -15
224 = 16x^2 -8x
You could rearrange and use the quadratic formula at this point, but we elect to "complete the square".
14 = x^2 -(1/2)x
14 +1/16 = x^2 -1/2x +(1/4)^2 . . . . . add the square of half the x-coefficient
(x -0.25)^2 = 14.0625
x = 0.25 ± 3.75 . . . . . . take the square root; add 0.25
Only positive values of x are useful here, so we have
x = 4
Then the dimensions are ...
length = 4x +3 = 4(4) +3 = 19 . . . feet
width = 4x -5 = 16 -5 = 11 . . . feet
