The equation 5/3x+11/3=−4/3 is solved as follows. Fill in the correct numbers to complete the solution.

Answer 1

To solve the equation $\frac{5}{3}x + \frac{11}{3} = \frac{-4}{3}$, we can start by isolating the variable $x$ on one side of the equation.

Let's begin by subtracting $\frac{11}{3}$ from both sides of the equation to eliminate the $\frac{11}{3}$ term on the left side:
\begin{align*}
\frac{5}{3}x + \frac{11}{3} - \frac{11}{3} &= \frac{-4}{3} - \frac{11}{3}\\
\frac{5}{3}x &= \frac{-15}{3}
\end{align*}

Now, we can simplify the right side of the equation:
\begin{align*}
\frac{5}{3}x &= \frac{-15}{3}
\end{align*}

To cancel out the coefficient $\frac{5}{3}$ on $x$, we can multiply both sides of the equation by its reciprocal, $\frac{3}{5}$:
\begin{align*}
\frac{3}{5}\cdot \frac{5}{3}x &= \frac{3}{5}\cdot \frac{-15}{3}\\
1x &= -\frac{45}{15}
\end{align*}

Now, we have:
\begin{align*}
x &= -\frac{45}{15}
\end{align*}

To simplify $\frac{45}{15}$, we can divide both the numerator and denominator by the greatest common divisor (GCD) of $45$ and $15$, which is $15$:
\begin{align*}
x &= -\frac{45}{15}\\
x &= -\frac{3}{1}
\end{align*}

Thus, the solution to the equation $\frac{5}{3}x + \frac{11}{3} = \frac{-4}{3}$ is $x = -\frac{3}{1}$.