Question

complete the steps to solve the equation $12x - \frac{2}{3} = 83\frac{1}{3}$.
$12x - \frac{2}{3} = 83\frac{1}{3}$ write the original equation.
$12x = \square$ apply the addition property of equality.
(simplify your answer.)

Explanation:

Step1: Identify the operation needed

To isolate the term with \( x \), we use the Addition Property of Equality, which states that if we add the same number to both sides of an equation, the equation remains true. Here, we need to add \( \frac{2}{3} \) to both sides to cancel out the \( -\frac{2}{3} \) on the left.

Step2: Perform the addition on both sides

Starting with the original equation:

$$ 12x - \frac{2}{3} = 83\frac{1}{3} $$

Add \( \frac{2}{3} \) to both sides:

$$ 12x - \frac{2}{3} + \frac{2}{3} = 83\frac{1}{3} + \frac{2}{3} $$

Simplify the left side (the \( -\frac{2}{3} \) and \( +\frac{2}{3} \) cancel):

$$ 12x = 83\frac{1}{3} + \frac{2}{3} $$

Now, add the mixed number and the fraction on the right. First, convert the mixed number \( 83\frac{1}{3} \) to an improper fraction (though we can also add the fractional parts directly). The fractional parts are \( \frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1 \). Then add that to the whole number part: \( 83 + 1 = 84 \). So:

$$ 12x = 84 $$

Answer:

\( 84 \)