Question

itional details were added for this assignment.
question
solve the following equation for ( x ):
( -1 = 2x + \frac{7}{3} )
select the correct answer below:
( -\frac{5}{3} )
( -\frac{2}{3} )
( -\frac{7}{6} )
( -\frac{1}{6} )
( -\frac{1}{2} )

Explanation:

Step1: Subtract $\frac{7}{3}$ from both sides

To isolate the term with \(x\), we subtract \(\frac{7}{3}\) from both sides of the equation \(-1 = 2x+\frac{7}{3}\).
\[
-1-\frac{7}{3}=2x+\frac{7}{3}-\frac{7}{3}
\]
Simplify the left - hand side: \(-1\) can be written as \(-\frac{3}{3}\), so \(-\frac{3}{3}-\frac{7}{3}=-\frac{3 + 7}{3}=-\frac{10}{3}\). The right - hand side simplifies to \(2x\). So we have \(-\frac{10}{3}=2x\).

Step2: Divide both sides by 2

To solve for \(x\), we divide both sides of the equation \(-\frac{10}{3}=2x\) by 2.
\[
x=\frac{-\frac{10}{3}}{2}
\]
Dividing by 2 is the same as multiplying by \(\frac{1}{2}\), so \(x =-\frac{10}{3}\times\frac{1}{2}\). When we multiply the numerators and denominators, we get \(x=-\frac{10\times1}{3\times2}=-\frac{5}{3}\).

Answer:

\(-\frac{5}{3}\) (the first option: \(\boldsymbol{-\frac{5}{3}}\))