The equation 53x+113=−43

Question

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.