—+5 + 6x = 2 + 5x + 3
Identity ( infinite solutions)
No solution
The given equation is:
5 + 6x = 2 + 5x + 3
Simplifying both sides, we get:
5 + 6x = 5 + 5x
Subtracting 5x from both sides, we get:
6x = 5x
Subtracting 5x from both sides, we get:
x = 0
Since this equation results in a single solution, x = 0, there is no infinite solution. Therefore, the correct answer is:
No solution.
To determine if the equation has infinite solutions or no solution, we need to simplify and evaluate the equation.
Given: -5 + 6x = 2 + 5x + 3
To simplify, we can combine like terms on both sides:
6x - 5x = 2 + 3 + 5
This simplifies to:
x = 10
Since the equation evaluates to a single value for x, there is only one solution. Therefore, the statement "No solution" is not correct. There is only a single solution for the equation.
To determine if the given equation has infinite solutions or no solution, we need to simplify the equation and see if it leads to a contradiction or an identity.
Let's simplify the given equation step by step:
- Start by combining like terms on both sides of the equation:
5 + 6x = 2 + 5x + 3
Now, we have:
5 + 6x = 5x + 5
- Next, let's rearrange the equation to isolate the variable term on one side:
6x - 5x = 5 - 5
Here, we subtract 5x from both sides and subtract 5 from both sides to simplify the equation:
x = 0
- Finally, let's substitute the value of x (which we found to be 0) back into the original equation to see if it holds true:
5 + 6(0) = 2 + 5(0) + 3
5 + 0 = 2 + 0 + 3
5 = 5
Since the equation is true for all values of x, the original equation is an identity. This means that the equation has infinite solutions, as any value of x will satisfy it.
Therefore, the answer is an identity (infinite solutions).