\[\frac{6}{7}(3-5n)\ge \frac{3}{5}(1-9n)\]
1
Simplify  67(3−5n)\frac{6}{7}(3-5n)  to  6(3−5n)7\frac{6(3-5n)}{7}.
6(3−5n)7≥35(1−9n)\frac{6(3-5n)}{7}\ge \frac{3}{5}(1-9n)

2
Simplify  35(1−9n)\frac{3}{5}(1-9n)  to  3(1−9n)5\frac{3(1-9n)}{5}.
6(3−5n)7≥3(1−9n)5\frac{6(3-5n)}{7}\ge \frac{3(1-9n)}{5}

3
Multiply both sides by 3535 (the LCM of 7,57, 5).
30(3−5n)≥21(1−9n)30(3-5n)\ge 21(1-9n)

4
Expand.
90−150n≥21−189n90-150n\ge 21-189n

5
Subtract 2121 from both sides.
90−150n−21≥−189n90-150n-21\ge -189n

6
Simplify  90−150n−2190-150n-21  to  −150n+69-150n+69.
−150n+69≥−189n-150n+69\ge -189n

7
Add 150n150n to both sides.
69≥−189n+150n69\ge -189n+150n

8
Simplify  −189n+150n-189n+150n  to  −39n-39n.
69≥−39n69\ge -39n

9
Divide both sides by −39-39.
−6939≤n-\frac{69}{39}\le n

10
Simplify  6939\frac{69}{39}  to  2313\frac{23}{13}.
−2313≤n-\frac{23}{13}\le n

11
Switch sides.
n≥−2313n\ge -\frac{23}{13}

Done

Decimal Form: -1.769231
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