To find the value that correctly fills in the blank so that the expressions are equivalent, we first need to calculate the left-hand side:
\( 42 + 70 = 112 \).
Now we need to find a value \( x \) such that:
\( (6 + 10) \cdot x = 112 \).
Starting with \( 6 + 10 \):
\( 6 + 10 = 16 \).
Now, let's set up the equation:
\( 16x = 112 \).
To find \( x \), we divide both sides by 16:
\( x = \frac{112}{16} \).
Calculating \( \frac{112}{16} \):
\( x = 7 \).
Thus, the value that correctly fills in the blank is 7.