# Calculate: (x-3)/(2)-(4x-3)/(3)-1=-(5x-12)/(6)

## Expression: $\frac{ x-3 }{ 2 }-\frac{ 4x-3 }{ 3 }-1=-\frac{ 5x-12 }{ 6 }$

Multiply both sides of the equation by $6$

$3\left( x-3 \right)-2\left( 4x-3 \right)-6=-\left( 5x-12 \right)$

Distribute $3$ through the parentheses

$3x-9-2\left( 4x-3 \right)-6=-\left( 5x-12 \right)$

Distribute $-2$ through the parentheses

$3x-9-8x+6-6=-\left( 5x-12 \right)$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$3x-9-8x+6-6=-5x+12$

Since two opposites add up to $0$, remove them from the expression

$3x-9-8x=-5x+12$

Collect like terms

$-5x-9=-5x+12$

Cancel equal terms on both sides of the equation

$-9=12$

The statement is false for any value of $x$

$∅$

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