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

Let's solve the equation step by step and fill in the blanks correctly:

1. Start with the equation:
\[
53x + 113 = -43
\]

2. **Subtract 113 from both sides**:
\[
53x = -43 - 113
\]

Calculate the right side:
\[
-43 - 113 = -156
\]

So we have:
\[
53x = -156
\]

3. **Divide both sides by 53** (instead of using "subtract 113"):
\[
x = \frac{-156}{53}
\]

4. We can simplify \(\frac{-156}{53}\) if needed, but for the purpose of filling in the blanks:
\[
x = -\frac{156}{53}
\]

5. Finally, if you meant to refer to multiplying by the reciprocal, then the steps should be:
\[
x = -\frac{156}{53} \cdot \frac{1}{53}
\]

The completed statements would be:
\[
53x + 113 = -43
\]
\[
53x = -156
\]
\[
x = -\frac{156}{53}
\]

If we write it in your format:
1. \(53x + 113 = -43\)
2. \(53x = -156\)
3. \(x = -\frac{156}{53}\)

You can fill in the final x using the fraction simplification if necessary.