Answer
The solution set is {n|n $\geq$ $\frac{7}{5}$ } , or [$\frac{7}{5}$, $\infty$) in interval notation.
Work Step by Step
We use the properties of inequalities to solve this inequality.
-2(n-1) $\leq$ 3(n-2) + 1
Use the distributive property.
-2n + 2 $\leq$ 3n -6 + 1
-2n + 2 $\leq$ 3n -5
5 + 2 $\leq$ 3n + 2n
7 $\leq$ 5n
Divide both sides by 7.
$\frac{7}{5}$ $\leq$ n
The solution set is {n|n $\geq$ $\frac{7}{5}$ } , or [$\frac{7}{5}$, $\infty$) in interval notation.
