How Many Solutions? Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items

Question
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 no solution.
The equation has no solution.

The equation has one solution: x=3

Answer 1

To determine how many solutions the equation \( 9(x+1) = 3(5x+1) - 12 \) has, we first simplify both sides of the equation.

1. Start with the original equation: \[ 9(x + 1) = 3(5x + 1) - 12 \]

2. Distribute on both sides: \[ 9x + 9 = 15x + 3 - 12 \] This simplifies to: \[ 9x + 9 = 15x - 9 \]

3. Now, let's get all the terms involving \( x \) on one side and constant terms on the other: \[ 9 + 9 = 15x - 9x \] This simplifies to: \[ 18 = 6x \]

4. Now, solve for \( x \): \[ x = \frac{18}{6} = 3 \]

Since we found a solution for \( x \), we conclude that the equation has one solution.

The answer is: The equation has one solution: \( x = 3 \).