First, we have to express algebraically the part "three consecutive integers".
[tex]x,x+1,x+2[/tex]According to the problem, these three consecutive integers have to sum 48. So, we can express the following equation.
[tex]x+x+1+x+2=48[/tex]Now, we solve for x
[tex]3x+3=48[/tex]We subtract 3 on each side-
[tex]\begin{gathered} 3x+3-3=48-3 \\ 3x=45 \end{gathered}[/tex]At last, we divide the equation by 3
[tex]\begin{gathered} \frac{3x}{3}=\frac{45}{3} \\ x=15 \end{gathered}[/tex]