Solve for x
x=2
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4\left(2x+1\right)=\left(3x-2\right)\left(1\times 4+1\right)
Variable x cannot be equal to \frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by 4\left(3x-2\right), the least common multiple of 3x-2,4.
8x+4=\left(3x-2\right)\left(1\times 4+1\right)
Use the distributive property to multiply 4 by 2x+1.
8x+4=\left(3x-2\right)\left(4+1\right)
Multiply 1 and 4 to get 4.
8x+4=\left(3x-2\right)\times 5
Add 4 and 1 to get 5.
8x+4=15x-10
Use the distributive property to multiply 3x-2 by 5.
8x+4-15x=-10
Subtract 15x from both sides.
-7x+4=-10
Combine 8x and -15x to get -7x.
-7x=-10-4
Subtract 4 from both sides.
-7x=-14
Subtract 4 from -10 to get -14.
x=\frac{-14}{-7}
Divide both sides by -7.
x=2
Divide -14 by -7 to get 2.
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