Answer
The solution is:
$$x = 2$$
To check if the solution is correct, we plus $2$ in for $x$ into the original equation:
$$\frac{(2)(2)}{3} = \frac{2}{6} + 1$$
Multiply all terms by their least common denominator, which is $6$ in this case, to get rid of the fractions:
$$6(\frac{4}{3}) = 6(\frac{2}{6}) + 6(1)$$
Simplify by dividing out common factors:
$$2(4) = 2 + 6$$
$$8 = 8$$
Both sides of the equation are equal, so the solution is correct.
Work Step by Step
We want to multiply all terms by their least common denominator, which is $6$ in this case, so we don't have to deal with fractions.
$$6(\frac{2x}{3}) = 6(\frac{x}{6}) + 6(1)$$
We divide out common factors to get rid of the fractions:
$$4x = x + 6$$
We subtract $x$ from both sides to isolate the variable:
$$3x = 6$$
Divide by $3$ on both sides to isolate $x$:
$$x = 2$$
To check if the solution is correct, we plus $2$ in for $x$ into the original equation:
$$\frac{(2)(2)}{3} = \frac{2}{6} + 1$$
Multiply all terms by their least common denominator, which is $6$ in this case, to get rid of the fractions:
$$6(\frac{4}{3}) = 6(\frac{2}{6}) + 6(1)$$
Simplify by dividing out common factors:
$$2(4) = 2 + 6$$
$$8 = 8$$
Both sides of the equation are equal, so the solution is correct.
