The equation 5/3x+11/3=−4/3 is solved as follows. Fill in the correct numbers to complete the solution.
To solve the equation 5/3x + 11/3 = -4/3, we need to isolate the variable x.
Step 1: Subtract 11/3 from both sides of the equation:
5/3x + 11/3 - 11/3 = -4/3 - 11/3
5/3x = -15/3
Step 2: Simplify both sides of the equation:
5/3x = -5
Now, to find the value of x, we need to get rid of the fraction. Multiply both sides of the equation by the reciprocal of the coefficient of x, which is 3/5.
(3/5) * (5/3x) = (3/5) * (-5)
On the left side, the (3/5) and (5/3) cancel each other out, leaving us with just x:
x = (3/5) * (-5)
Now, multiply the numerators and denominators:
x = -15/5
Simplify the fraction:
x = -3
So the solution to the equation 5/3x + 11/3 = -4/3 is x = -3.
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 $x = -\frac{3}{1}$.
To solve the equation 5/3x + 11/3 = -4/3, we need to isolate the variable x.
Step 1: Subtract 11/3 from both sides of the equation to move the constant term to the right side:
5/3x + 11/3 - 11/3 = -4/3 - 11/3
Simplifying:
5/3x = -15/3
Step 2: Simplify the right side of the equation:
5/3x = -5
Step 3: Multiply both sides of the equation by the reciprocal of 5/3, which is 3/5:
(3/5)(5/3)x = (3/5)(-5)
Simplifying:
1x = -3
Step 4: Simplify:
x = -3
Therefore, the solution to the equation 5/3x + 11/3 = -4/3 is x = -3.