Question

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 \( \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \), let's fill in the steps:

1. Start by isolating the term with \( x \) on one side. To do this, subtract \( \frac{11}{3} \) from both sides:

\[ \frac{5}{3}x = -\frac{4}{3} - \frac{11}{3} \]

Now, let's simplify the right side:

\[ -\frac{4}{3} - \frac{11}{3} = -\frac{4 + 11}{3} = -\frac{15}{3} = -5 \]

So, we have:

\[ \frac{5}{3}x = -5 \]

2. Now, multiply both sides by \( \frac{3}{5} \), the reciprocal of \( \frac{5}{3} \):

\[ x = -5 \cdot \frac{3}{5} \]

Calculating the right side:

\[ x = -\frac{5 \cdot 3}{5} = -3 \]

So, the completed solution would be:

\[ 5/3x + 11/3 = -4/3 \] \[ 5/3x = -5 \] \[ x = -3 \]