The distributive property states:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]
therefore:
[tex]\begin{gathered} \frac{1}{2}(8x+7)+\frac{1}{2}=\frac{1}{2}\cdot8x+\frac{1}{2}\cdot7+\frac{1}{2}=4x+\frac{7}{2}+\frac{1}{2}=4x+\frac{7+1}{2}=4x+\frac{8}{2} \\ so\colon \\ 4x+\frac{8}{2}=4x+4=4(x+1) \end{gathered}[/tex]
