Question

what is the solution for the equation?
( a + \frac{8}{3} = \frac{2}{3} )
( a = -\frac{10}{3} )
( a = -2 )
( a = 2 )
( a = \frac{10}{3} )

Explanation:

Step1: Isolate the variable \(a\)

To solve for \(a\) in the equation \(a+\frac{8}{3}=\frac{2}{3}\), we need to subtract \(\frac{8}{3}\) from both sides of the equation. This is based on the addition property of equality, which states that if we add or subtract the same number from both sides of an equation, the equation remains true. So we have:
\(a+\frac{8}{3}-\frac{8}{3}=\frac{2}{3}-\frac{8}{3}\)

Step2: Simplify both sides

Simplifying the left - hand side, \(a+\frac{8}{3}-\frac{8}{3}=a\).
For the right - hand side, we use the rule for subtracting fractions with the same denominator: \(\frac{a - b}{c}=\frac{a}{c}-\frac{b}{c}\) (where \(c
eq0\)). So \(\frac{2}{3}-\frac{8}{3}=\frac{2 - 8}{3}=\frac{-6}{3}=- 2\).

Answer:

\(a = - 2\) (corresponding to the option \(a=-2\))