The inequality given is
[tex]11x+4\mleft(x-2\mright)<5x+2[/tex]Step 1: Expand the bracket
[tex]\begin{gathered} 11x+4\mleft(x-2\mright)<5x+2 \\ 11x+4x-8<5x+2 \end{gathered}[/tex]Step 2: collect similar terms
[tex]\begin{gathered} 11x+4x-8<5x+2 \\ 15x-8<5x+2 \end{gathered}[/tex]Step 3: Add 8 to both sides
[tex]\begin{gathered} 15x-8<5x+2 \\ 15x-8+8<5x+2+8 \\ 15x<5x+10 \end{gathered}[/tex]Step 4: Substract 5x from both sides
[tex]\begin{gathered} 15x<5x+10 \\ 15x-5x<5x+10-5x \\ 10x<10 \end{gathered}[/tex]Step 5: Divide both sides by 10
[tex]\begin{gathered} \frac{10x}{10}<\frac{10}{10} \\ x<1 \end{gathered}[/tex]Hence,
[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: x<1\: \\ \: \mathrm{Interval\: Notation\colon} & \: \mleft(-\infty\: ,\: 1\mright)\end{bmatrix}\text{ }[/tex]Therefore,
The solution = x<1
The interval notattion = (-∞,1)
