Answer:
The blank is 3
Step-by-step explanation:
1 - Give the blank a variable
x = our blank
2 - Write it out
[tex]\frac{5}{7} + \frac{x}{6} = \frac{51}{42}[/tex]
3 - Get the denominators equal
[tex]\frac{5}{7}(\frac{6}{6}) +\frac{x}{6}(\frac{7}{7}) = \frac{51}{42} \\\frac{30}{42}+\frac{7x}{42} = \frac{51}{42}[/tex]
4 - Simplify
[tex]\frac{30+7x}{42} = \frac{51}{42} \\ \frac{30+7x}{42} = \frac{51}{42}[/tex]
5 - Solve for the numerators
30+7x = 51
-30 -30
7x = 21
x = 3
