Answer:
[tex]w\geq -4[/tex]
[tex]\{w\:|\:w\geq -4\}[/tex]
[tex][-4,\infty)[/tex]
Step-by-step explanation:
Given inequality:
[tex]2\geq -\dfrac{3}{2}w-4[/tex]
To solve the inequality, begin by adding 4 to both sides:
[tex]2+4\geq -\dfrac{3}{2}w-4+4\\\\\\ 6\geq -\dfrac{3}{2}w[/tex]
Now, multiply both sides by 2:
[tex]6\cdot 2\geq -\dfrac{3}{2}w\cdot 2\\\\\\12\geq-3w[/tex]
Finally divide both sides by -3, remembering to reverse the inequality sign as we are dividing by a negative number:
[tex]\dfrac{12}{-3}\leq \dfrac{-3w}{-3}\\\\\\-4\leq w\\\\\\w\geq -4[/tex]
Therefore, the solution to the inequality is:
[tex]\Large\text{$w\geq -4$}[/tex]
Graphically, this represents all values of w that are greater than or equal to -4 on the number line. (See attachment).
In set-builder notation, the solution set is:
[tex]\Large\text{$\{w\:|\:w\geq -4\}$}[/tex]
In interval notation, it is:
[tex]\Large\text{$[-4,\infty)$}[/tex]
