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 one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .
The equation has no solution.
11x=3(7x−1)−10x
Simplifying the equation:
11x = 21x - 3 - 10x
Combining like terms:
11x = 11x - 3
Subtracting 11x from both sides:
0 = -3
Since 0 is not equal to -3, the equation has no solution.
To determine if the equation has one, none, or infinite solutions, we need to simplify the equation and check if there is a unique value for x or if any values of x satisfy the equation.
Given equation: 11x = 3(7x - 1) - 10x
First, distribute the 3 to the terms inside the parentheses:
11x = 21x - 3 - 10x
Combining like terms on the right side:
11x = 11x - 3
Next, subtract 11x from both sides to isolate x:
11x - 11x = -3
Simplifying,
0x = -3
Since 0x is always equal to 0 and it cannot equal -3, there are no values of x that satisfy the equation.
Therefore, the equation has no solution.
To solve this equation, we need to simplify it and collect like terms. Let's start by distributing the 3 to the terms inside the parentheses:
11x = 3(7x - 1) - 10x
11x = 21x - 3 - 10x
Next, combine like terms on the right side of the equation:
11x = 11x - 3
At this point, notice that the x terms cancel out on both sides of the equation. This leaves us with -3 = -3.
Since -3 is equal to -3, this means that the equation is true for any value of x. Therefore, the equation has infinite solutions.