Question

How many solutions exist for the given equation?
3x + 13 = 3(x + 6) + 1
A. zero
B. one
C. two
D. infinitely many

Answer 1

3x + 13 = 3(x + 6) + 1

First distribute 3 through the parenthesis:

3x + 13 = 3(x + 6) + 1

Next cancel equal terms on both sides of the equation:

3x + 13 = 3x + 18 + 1

13 = 18 + 1

Finally add the numbers:

13 = 18 + 1

13 = 19

Answer 2

Evaluating the equation using algebraic principle, the LHS ≠ RHS ; Hence, the equation has Zero solution.

Evaluating the expression :

3x + 13 = 3(x + 6) + 1

We check if RHS = LHS

3x + 13 = 3x + 18 + 1

3x + 13 = 3x + 17

3x cancels out

13 = 17

This means that RHS ≠ LHS ;

Therefore, the equation has no solution.

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