how many solutions does 11x=3(7x−1)−10x have?
To find the number of solutions, we need to solve the equation and see how many values of x satisfy the equation.
Starting with the given equation:
11x = 3(7x - 1) - 10x
First, distribute 3 to the terms inside the parentheses:
11x = 21x - 3 - 10x
Combine like terms:
11x = 11x - 3
Rearrange the equation:
11x - 11x = -3
0 = -3
This equation states that 0 is equal to -3, which is false. Therefore, there are no solutions to this equation.
To determine the number of solutions for the given equation 11x = 3(7x - 1) - 10x, we will solve it step-by-step.
Step 1: Distribute the 3 to the terms within the parentheses.
11x = 21x - 3 - 10x
Step 2: Combine like terms on the right side of the equation.
11x = 11x - 3
Step 3: Subtract 11x from both sides of the equation.
11x - 11x = -3
Step 4: Simplify and solve for x.
0 = -3
The equation 0 = -3 implies that there is no value of x that satisfies the equation. Therefore, the given equation has no solutions.
To find out how many solutions the equation 11x = 3(7x-1) - 10x has, we need to simplify it and see if it leads to a true statement or a contradiction.
Step 1: Distribute the 3 to (7x-1):
11x = 21x - 3 - 10x
Step 2: Combine like terms on the right side:
11x = 11x - 3
Step 3: Move all terms involving x to one side and all constant terms to the other side:
11x - 11x = -3
Step 4: Simplify:
0 = -3
Now, we need to analyze the result. Since we end up with a contradiction (0 does not equal -3), this means that the equation has no solution or is inconsistent.
Therefore, the equation 11x = 3(7x-1) - 10x has no solution.