Plug a few points into the original equations and check to show that they can have no solution. Explain your work. 2x+3=2x+7, 5x+5=5x+4
For the equation 2x+3=2x+7, we can simplify it as follows:
2x + 3 = 2x + 7
2x - 2x + 3 = 2x - 2x + 7
0x + 3 = 0x + 7
3 = 7
Since the equation simplifies to 3 = 7, it means that the two sides of the equation are not equal. Therefore, there is no solution.
Now let's analyze the equation 5x+5=5x+4:
5x + 5 = 5x + 4
5x - 5x + 5 = 5x - 5x + 4
0x + 5 = 0x + 4
5 = 4
Similar to the previous equation, we end up with 5 = 4, which shows that the equation is not true. Therefore, there is no solution.
In both cases, by simplifying the equations we obtain contradictions, which means the original equations have no solution.
To determine if the given equations have no solution, we can plug in a few points into the equations and see if the equations hold true.
1. For the equation 2x + 3 = 2x + 7:
Let's subtract 2x from both sides of the equation:
2x - 2x + 3 = 2x - 2x + 7
3 = 7
Since 3 is not equal to 7, the equation is not true. Therefore, the equation has no solution.
2. For the equation 5x + 5 = 5x + 4:
Let's subtract 5x from both sides of the equation:
5x - 5x + 5 = 5x - 5x + 4
5 = 4
Again, 5 is not equal to 4, so the equation is not true. Hence, this equation also has no solution.
In both cases, we arrive at a contradiction which confirms that the equations have no solution.
To determine whether these equations have no solution, we can plug in values for 'x' and check if the equations hold true.
Let's start with the first equation: 2x + 3 = 2x + 7
If we subtract 2x from both sides of the equation, we get:
3 = 7
Here we can see that the equation becomes 3 = 7, which is not true. Therefore, there is no value of 'x' that would satisfy this equation. In other words, it has no solution.
Now let's move on to the second equation: 5x + 5 = 5x + 4
If we subtract 5x from both sides of the equation, we get:
5 = 4
Once again, we can see that the equation becomes 5 = 4, which is not true. Hence, this equation also has no solution.
These examples demonstrate that when the variables cancel out during algebraic operations, we end up with statements that are not true (such as 3 = 7 or 5 = 4). Therefore, we conclude that both equations have no solutions.