Question

The equation 5/3x+11/3=−4/3
is solved as follows. Fill in the correct numbers to complete the solution.(1 point)
5/3x+11/3=−4/3
5?3x=

Subtract 11/3
from both sides.
x=

Multiply both sides by 3/5
, the reciprocal of 5/3
.

Answer 1

To solve the equation \( \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \), we can follow the steps outlined and fill in the numbers as needed.

1. Start with the original equation:
\[
\frac{5}{3}x + \frac{11}{3} = -\frac{4}{3}
\]

2. Subtract \( \frac{11}{3} \) from both sides:
\[
\frac{5}{3}x = -\frac{4}{3} - \frac{11}{3}
\]

To combine the terms on the right side, we have:
\[
-\frac{4}{3} - \frac{11}{3} = -\frac{4 + 11}{3} = -\frac{15}{3} = -5
\]

So we have:
\[
\frac{5}{3}x = -5
\]

3. Multiply both sides by \( \frac{3}{5} \), the reciprocal of \( \frac{5}{3} \):
\[
x = -5 \times \frac{3}{5}
\]

Simplifying that gives:
\[
x = -3
\]

To summarize the filled-in parts:

1. \( \frac{5}{3}x = -5 \)
2. \( x = -3 \)

So, the complete steps are:
- \( 5/3x = -5 \)
- \( x = -3 \)