Question

a) 3(x+1)+x+2=2(2x+1)+3
I distributed the equation and got 5=5 as my final answer.

b) DON'T UNDERSTAND
is the resulting equation from part (a) always true,sometimes ture, or never true? Explain your reasoning.

Answer 1

please help me

Answer 2

If you solve an equation and your variables drop out like in the one above, two cases are possible

1. the resulting statement is true , in which case your equation was an "identity" , and it is true for all values of the variable

or

2. the resulting statement is false, in which case there is no solution at all to your equation

e.g. If your equation had been
3(x+1)+x+2=2(2x+1)+2
you would end up with
5 = 4, a false statement.
Thus your equation would have no solution.

So for your given equation, the statement is always true.