The equation 53x+113=−43

Question

is solved as follows. Fill in the correct numbers to complete the solution.(1 point)
53x+113=−43
53x=

Subtract 113
from both sides.
x=

Multiply both sides by 35
, the reciprocal of 53
.

Answer 1

To solve the equation \( 53x + 113 = -43 \), we can follow these steps:

1. Subtract 113 from both sides: \[ 53x + 113 - 113 = -43 - 113 \] This simplifies to: \[ 53x = -156 \]

2. Now, divide both sides by 53 (which is the same as multiplying by its reciprocal, \( \frac{1}{53} \)): \[ x = \frac{-156}{53} \]

So, filling in the blanks in your format:

1. \( 53x = -156 \) after subtracting 113 from both sides.
2. \( x = \frac{-156}{53} \) after dividing by 53.

Thus, the complete statements would be:

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

(Note: The multiplication by 35 mentioned in your question seems to be a typo; it should refer to multiplying by \( \frac{1}{53} \), not 35.)