We are given the following inequality:
[tex]3x+2\le5(x-4)[/tex]First, we will apply the distributive property on the term on the right side of the inequality:
[tex]3x+2\le5x-20[/tex]Now we will subtract 5x to both sides:
[tex]\begin{gathered} 3x-5x+2\le-20 \\ -2x+2\le-20 \end{gathered}[/tex]Now we will subtract 2 to both sides:
[tex]\begin{gathered} -2x\le-20-2 \\ -2x\le-22 \end{gathered}[/tex]Dividing both sides by -2, since we are dividing by a negative number we need to invert the direction of the inequality sign:
[tex]\begin{gathered} x\ge-\frac{22}{-2} \\ \\ x\ge11 \end{gathered}[/tex]Therefore, the solution is x >= 11
