Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x (1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .
To solve the equation, we can simplify it first:
11x = 3(7x - 1) - 10x
11x = 21x - 3 - 10x
11x = 11x - 3
Now, we notice that both sides of the equation have the same term (11x). This means that the equation is an identity and will be true for any value of x. Therefore, the equation has infinite solutions.
The correct response is:
The equation has infinite solutions.
To determine if the equation 11x=3(7x-1)-10x has one, none, or infinite solutions, we need to simplify and solve for x.
Expanding the brackets on the right side, we get:
11x = 21x - 3 - 10x
Combining like terms on the right side, we have:
11x = 11x - 3
Subtracting 11x from both sides, we get:
0 = -3
Since -3 is not equal to 0, the equation has no solution.
Therefore, the correct response is: The equation has no solution.
To solve the equation and determine if it has one, none, or infinite solutions, follow these steps:
Step 1: Distribute on the right side of the equation.
- Rewrite the equation: 11x = 3(7x - 1) - 10x.
- Distribute the 3: 11x = 21x - 3 - 10x.
Step 2: Combine like terms.
- Combine the x terms on the right side: 11x = 21x - 10x - 3.
- Simplify the equation: 11x = 11x - 3.
Step 3: Continue simplifying.
- Subtract 11x from both sides of the equation: 0 = -3.
Step 4: Analyze the result.
- The equation 0 = -3 is false since zero cannot equal a non-zero number like -3.
- This means there is no solution to the equation.
Therefore, the correct answer is: The equation has no solution.