Solve for x
x
to determine if the equation has one, none, or infinite solutions.
9(x+1)=3(5x+1)−12
9
(
x
+
1
)
=
3
(
5
x
+
1
)
−
12
(1 point)
Responses
The equation has one solution: x=0
.
The equation has one solution: x equals 20 .
The equation has one solution: x=3
.
The equation has one solution: x equals 3 .
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
To solve the equation 9(x+1)=3(5x+1)-12:
First, simplify both sides of the equation:
9(x+1) = 3(5x+1) - 12
9x + 9 = 15x + 3 - 12
Next, move all the x terms to one side and all the constant terms to the other side:
9 - 3 = 15x - 9x + 3 - 12
6 = 6x - 9
Add 9 to both sides:
6 + 9 = 6x - 9 + 9
15 = 6x
Finally, divide both sides by 6 to isolate x:
15/6 = (6x)/6
Simplify:
5/2 = x
So the equation has one solution: x = 5/2 or x = 2.5
To solve the equation 9(x+1)=3(5x+1)-12, let's simplify the expression on both sides step by step:
Step 1: Distribute on both sides:
9x + 9 = 15x + 3 - 12
Step 2: Combine like terms:
9x + 9 = 15x - 9
Step 3: Move all the x terms to one side and the constant terms to the other side:
9x - 15x = -9 - 9
Step 4: Combine like terms:
-6x = -18
Step 5: Divide both sides by -6 to solve for x:
(-6x)/(-6) = (-18)/(-6)
x = 3
Therefore, the equation has one solution: x = 3.