We are given the following inequality
[tex]14\le2-4v[/tex]
We are asked to solve this inequality for v.
Our goal is to separate the variable v.
Step 1:
Subtract 2 from both sides of the inequality
[tex]\begin{gathered} 14-2\le2-2-4v \\ 12\le-4v \end{gathered}[/tex]
Step 2:
Divide both sides of the inequality by 4
[tex]\begin{gathered} \frac{12}{4}\le-\frac{4v}{4} \\ 3\le-v \end{gathered}[/tex]
Step 3:
Multiply both sides of the inequality by -1 (the inequality sign will be reversed)
[tex]\begin{gathered} 3(-1)\le-v(-1) \\ -3\ge v \end{gathered}[/tex]
Step 4:
Finally, shift the variables (the inequality sign will be reversed)
[tex]\begin{gathered} -3\ge v \\ v\le-3 \end{gathered}[/tex]
Therefore, the solution of the inequality is
[tex]v\le-3[/tex]
