\[\frac{x+3}{2}\ge \frac{2}{3}\]
1
Multiply both sides by 22.
x+3≥23×2x+3\ge \frac{2}{3}\times 2

2
Use this rule: ab×c=acb\frac{a}{b} \times c=\frac{ac}{b}.
x+3≥2×23x+3\ge \frac{2\times 2}{3}

3
Simplify  2×22\times 2  to  44.
x+3≥43x+3\ge \frac{4}{3}

4
Subtract 33 from both sides.
x≥43−3x\ge \frac{4}{3}-3

5
Simplify  43−3\frac{4}{3}-3  to  −53-\frac{5}{3}.
x≥−53x\ge -\frac{5}{3}

Done

Decimal Form: -1.666667
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