$$\frac{ 2x-1 }{ 4 } + \frac{ 3x-2 }{ 3 } =2 \frac{ 1 }{ 2 }$$
$x = \frac{41}{18} = 2\frac{5}{18} \approx 2.277777778$
$$3\left(2x-1\right)+4\left(3x-2\right)=6\left(2\times 2+1\right)$$
$$6x-3+4\left(3x-2\right)=6\left(2\times 2+1\right)$$
$$6x-3+12x-8=6\left(2\times 2+1\right)$$
$$18x-3-8=6\left(2\times 2+1\right)$$
$$18x-11=6\left(2\times 2+1\right)$$
$$18x-11=6\left(4+1\right)$$
$$18x-11=6\times 5$$
$$18x-11=30$$
$$18x=30+11$$
$$18x=41$$
$$x=\frac{41}{18}$$
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