$$\frac { x - 3 } { 4 } - \frac { x + 2 } { 3 } = 1 - \frac { x + 1 } { 5 }$$
$x=19$
$$15\left(x-3\right)-20\left(x+2\right)=60-12\left(x+1\right)$$
$$15x-45-20\left(x+2\right)=60-12\left(x+1\right)$$
$$15x-45-20x-40=60-12\left(x+1\right)$$
$$-5x-45-40=60-12\left(x+1\right)$$
$$-5x-85=60-12\left(x+1\right)$$
$$-5x-85=60-12x-12$$
$$-5x-85=48-12x$$
$$-5x-85+12x=48$$
$$7x-85=48$$
$$7x=48+85$$
$$7x=133$$
$$x=\frac{133}{7}$$
$$x=19$$
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