Let's solve the equation step by step to fill in the blanks correctly.
The original equation is:
\[ \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \]
Step 1: Subtract \(\frac{11}{3}\) from both sides
Starting with:
\[ \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \]
Subtracting \(\frac{11}{3}\) from both sides gives:
\[ \frac{5}{3}x = -\frac{4}{3} - \frac{11}{3} \]
Now, we need to add the fractions on the right side:
\[ -\frac{4}{3} - \frac{11}{3} = -\frac{4 + 11}{3} = -\frac{15}{3} = -5 \]
So, we have:
\[ \frac{5}{3}x = -5 \]
Step 2: Multiply both sides by the reciprocal of \(\frac{5}{3}\)
Now to solve for \(x\):
\[ x = -5 \cdot \frac{3}{5} \]
Multiplying gives:
\[ x = -\frac{15}{5} = -3 \]
Final Answers to Fill in the Blanks
Putting everything together, we fill in the blanks:
- For \(\frac{5}{3}x =\) -5
- For \(x =\) -3
So the complete solution is:
\[ \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3}
\frac{5}{3}x = -5 \text{ Subtract } \frac{11}{3} \text{ from both sides}
x = -3 \text{ Multiply both sides by } \frac{3}{5}, \text{ the reciprocal of } \frac{5}{3} \]