If we consider the equation 2x + 3 = 2x + 7, we can plug in any value for x and see that the equation is always true. For example, if we choose x = 1, we would have:
2(1) + 3 = 2(1) + 7
2 + 3 = 2 + 7
5 = 9 (which is false)
No matter what value we choose for x, the equation will always result in a false statement. Therefore, this equation has no solution.
Similarly, if we consider the equation 5x + 5 = 5x + 4 and plug in any value for x, we can see that the equation is never true. For example, if we choose x = 1:
5(1) + 5 = 5(1) + 4
5 + 5 = 5 + 4
10 = 9 (which is false)
No matter what value we choose for x, the equation will always result in a false statement. Therefore, this equation also has no solution.
In both cases, the equations are such that the variable x cancels out on both sides of the equation, resulting in an equation that is always false. This means there is no value of x that will satisfy the equation, hence no solution.
Plug a few points into 2x+3=2x+7,5x+5=5x+4 then check to show that they can have no solution. Explain your work.
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