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\left(x-6\right)\times 5-\left(2x+1\right)\times 2=4
Variable x cannot be equal to any of the values -\frac{1}{2},6 since division by zero is not defined. Multiply both sides of the equation by \left(x-6\right)\left(2x+1\right), the least common multiple of 2x+1,x-6,2x^{2}-11x-6.
5x-30-\left(2x+1\right)\times 2=4
Use the distributive property to multiply x-6 by 5.
5x-30-\left(4x+2\right)=4
Use the distributive property to multiply 2x+1 by 2.
5x-30-4x-2=4
To find the opposite of 4x+2, find the opposite of each term.
x-30-2=4
Combine 5x and -4x to get x.
x-32=4
Subtract 2 from -30 to get -32.
x=4+32
Add 32 to both sides.
x=36
Add 4 and 32 to get 36.