Let's solve the equation step by step and fill in the missing parts.
Starting with the given equation:
\[ \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \]
Step 1: Subtract \(\frac{11}{3}\) from both sides.
\[ \frac{5}{3}x = -\frac{4}{3} - \frac{11}{3} \]
Combine the fractions on the right side:
\(-\frac{4}{3} - \frac{11}{3} = -\frac{15}{3}\)
Therefore,
\[ \frac{5}{3}x = -\frac{15}{3} \]
So, the first blank is filled:
\[ 5/3x = -\frac{15}{3} \]
Step 2: Now, divide both sides by \(\frac{5}{3}\) to solve for \(x\), which is the same as multiplying both sides by the reciprocal of \(\frac{5}{3}\), which is \(\frac{3}{5}\).
Thus,
\[ x = -\frac{15}{3} \cdot \frac{3}{5} \]
Now simplify the right side:
\(-\frac{15}{3} \cdot \frac{3}{5} = -\frac{15 \cdot 3}{3 \cdot 5} = -\frac{15}{5} = -3\)
So, the second blank is filled:
\[ x = -3 \]
Putting it all together, here are the filled in parts:
- \(\frac{5}{3}x = -\frac{15}{3}\)
- \(x = -3\)
Final Summary:
- After subtracting \(\frac{11}{3}\) we get: \(5/3x = -\frac{15}{3}\)
- Then, multiplying both sides by \(\frac{3}{5}\) gives \(x = -3\).
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