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.

1 answer

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