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

Zero solution or with the symbol ∅.

The goal of this case is solving linear equations, i.e., distributive property.

We will find out how many solutions exist for the given equation.

We use the multiplication distribution by multiplying 3 into parentheses.

Then we add up the same terms on the right hand side.

Finally, we subtract both sides by 3x.

Up to this step, we receive a false statement. The term x is gone and what remains is the term of constants. Hence, the equation has no solutions (or zero solution).

If an equation has no solutions, we write for the solution set. That symbol means the null set (or empty set).

Other examples

(1). 3x + 2 = 2(x + 1)

(2). x(x - 1) = x

(3). 2(x + 1) - x = 3x - 2(x - 1)

(4). 2(x - 1) - x = 3x - 2(x - 1)

Keywords: how many solutions, exist for the given equation, 3x + 13 = 3(x + 6) + 1, zero, one, two, infinitely, many, solving linear equations, distributive property, empty set, null

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: