Question

The equation 53x+113=−43
5
3
𝑥
+
11
3
=
−
4
3
is solved as follows. Fill in the correct numbers to complete the solution.(1 point)
53x+113=−43
5
3
𝑥
+
11
3
=
−
4
3
53x=
5
3
𝑥
=
Subtract 113
11
3
from both sides.
x=
𝑥
=
Multiply both sides by 35
3
5
, the reciprocal of 53
5
3
.

Answer 1

Sure! Let's go through the solution step by step for the equation \( 53x + 113 = -43 \).

1. Start with the original equation:

\[
53x + 113 = -43
\]

2. Subtract \( 113 \) from both sides:

\[
53x = -43 - 113
\]

Simplifying the right side:

\[
53x = -156
\]

3. Now, divide both sides by \( 53 \):

\[
x = \frac{-156}{53}
\]

4. Simplifying further:

The fraction \( \frac{-156}{53} \) can be simplified depending on whether it's reducible or not, but since \( 156 \div 53 \) does not yield an integer, we keep it as:

\[
x = -\frac{156}{53}
\]

5. Now let's multiply both sides by the reciprocal of \( 53 \), which is \( \frac{1}{53} \):

The formal statement would look something like:

\[
x = \left(-\frac{156}{53}\right) \cdot \left(\frac{1}{53}\right)
\]

Thus, the filled-in numbers are:

1. \( 53x = -156 \)
2. \( x = -\frac{156}{53} \)

So to summarize:

\[
53x + 113 = -43 \\
53x = -156 \quad \text{(Subtract 113 from both sides)} \\
x = -\frac{156}{53} \quad \text{(Divide both sides by } 53\text{)}
\]