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6\left(x-4\right)-\left(x-3\right)=144
Multiply both sides of the equation by 12, the least common multiple of 2,12.
6x-24-\left(x-3\right)=144
Use the distributive property to multiply 6 by x-4.
6x-24-x-\left(-3\right)=144
To find the opposite of x-3, find the opposite of each term.
6x-24-x+3=144
The opposite of -3 is 3.
5x-24+3=144
Combine 6x and -x to get 5x.
5x-21=144
Add -24 and 3 to get -21.
5x=144+21
Add 21 to both sides.
5x=165
Add 144 and 21 to get 165.
x=\frac{165}{5}
Divide both sides by 5.
x=33
Divide 165 by 5 to get 33.