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4x+x-7=3x-6
Multiply both sides of the equation by 6, the least common multiple of 3,6.
5x-7=3x-6
Combine 4x and x to get 5x.
5x-7-3x=-6
Subtract 3x from both sides.
2x-7=-6
Combine 5x and -3x to get 2x.
2x=-6+7
Add 7 to both sides.
2x=1
Add -6 and 7 to get 1.
x=\frac{1}{2}
Divide both sides by 2.