Solve for x
to determine if the equation has one, none, or infinite solutions.
9(x+1)=3(5x+1)−12
(1 point)
Responses
The equation has one solution: x=0
.
The equation has one solution: x equals 20 .
The equation has infinite solutions.
The equation has infinite solutions.
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.
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page 12 of 13
To solve the equation, we first simplify both sides:
9(x+1) = 3(5x+1) − 12
9x+9 = 15x+3 - 12
Next, we combine like terms on each side:
9x - 15x = 3 - 12 - 9
-6x = -18
x = -18 / -6
x = 3
Therefore, the equation has one solution: x = 3
To solve the equation 9(x+1) = 3(5x+1) - 12:
Step 1: Distribute on both sides of the equation.
9x + 9 = 15x + 3 - 12
Step 2: Combine like terms.
9x + 9 = 15x - 9
Step 3: Move all the variables to one side and all the constants to the other side.
9x - 15x = -9 - 9
Step 4: Simplify.
-6x = -18
Step 5: Divide both sides of the equation by -6 to solve for x.
x = (-18) / (-6)
Step 6: Simplify.
x = 3
Therefore, the equation has one solution: x = 3.