What happens if you replace c with a number other than 5?
c ≠ 5, see solution.
Practice makes perfect
We are given the following equation.
3x-5=3x-c
If we look closely, we see that the x-terms on both sides are the same. Only the constants look different.
3x-5= 3x-c
If we substitute 5 for c, we get an identity. This means that the equation holds true for all values of x, as the left-hand side and right-hand side are identical.
3x-5=3x- 5
We can substitute any value for x and the equation will remain true. Let's try x= 0.
We see the equation remained true. However, if c ≠ 5, the equation has no solution. The reason for that is that the left-hand side will never equal the right-hand side, no matter what value we substitute for x. Let's pick c= 1 and try to solve the equation.
The equation is false after simplifying, which means it has no solutions. This will be the case for all values of c that are different from 5. We can simply say that the equation has no solution if c ≠ 5.
