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

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 $156÷53$ 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:

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

Thus, the filled-in numbers are:

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

So to summarize:

$$53x+113=-4353x=-156\text{(Subtract 113 from both sides)}x=-\frac{156}{53}\text{(Divide both sides by }53\text{)}$$