Question

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

Subtract 11/3
from both sides.
x=

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

Answer 1

Let's solve the equation step by step and fill in the missing numbers.

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 fractions on the right side:
\[
-\frac{4 + 11}{3} = -\frac{15}{3}
\]
Therefore:
\[
\frac{5}{3} x = -5
\]

3. Now, complete the equation for \(x\):
\[
x = -5
\]
Multiply both sides by \(\frac{3}{5}\) (the reciprocal of \(\frac{5}{3}\)):
\[
x = -5 \cdot \frac{3}{5}
\]
\[
x = -3
\]

So the complete solution can be summarized as follows:

1. Fill in the subtraction result:
\[
5/3 x = -5
\]

2. Fill in the value of \(x\):
\[
x = -3
\]

Thus the final filled-in statements would be:
- \(5/3 x = -5\)
- \(x = -3\)