A house has a front yard with an area of 4,200 ft.2 . The area of the house plus the area of the yard is 8 times the area of the house alone. What equation does this real-world situation model? Use A for the area of the house.(1 point)
A + 4,200 = 8A
Solve for X
1. 9x + 16 = 6x + 1
2. 4x - 3 = 3x - 9
3. 3x - 3 = 6x + 18
1. To solve for x, we want to isolate it on one side of the equation.
9x + 16 = 6x + 1
Subtract 6x from both sides:
9x - 6x + 16 = 6x - 6x + 1
Simplify:
3x + 16 = 1
To isolate x, subtract 16 from both sides:
3x + 16 - 16 = 1 - 16
Simplify:
3x = -15
Finally, divide both sides by 3:
x = -15/3
x = -5
Therefore, x equals -5.
2. To solve for x in the second equation, we will follow the same steps:
4x - 3 = 3x - 9
Subtract 3x from both sides:
4x - 3x - 3 = 3x - 3x - 9
Simplify:
x - 3 = -9
To isolate x, add 3 to both sides:
x - 3 + 3 = -9 + 3
Simplify:
x = -6
So, x equals -6.
3. To solve the third equation, we again follow the same steps:
3x - 3 = 6x + 18
Subtract 6x from both sides:
3x - 6x - 3 = 6x - 6x + 18
Simplify:
-3x - 3 = 18
To isolate x, add 3 to both sides:
-3x - 3 + 3 = 18 + 3
Simplify:
-3x = 21
Finally, divide both sides by -3:
x = 21/-3
x = -7
Thus, x equals -7.