Solve for x
x = -\frac{14}{3} = -4\frac{2}{3} \approx -4.666666667
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\left(2x+1\right)\times 4=\left(x-2\right)\times 5
Variable x cannot be equal to any of the values -\frac{1}{2},2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(2x+1\right), the least common multiple of x-2,2x+1.
8x+4=\left(x-2\right)\times 5
Use the distributive property to multiply 2x+1 by 4.
8x+4=5x-10
Use the distributive property to multiply x-2 by 5.
8x+4-5x=-10
Subtract 5x from both sides.
3x+4=-10
Combine 8x and -5x to get 3x.
3x=-10-4
Subtract 4 from both sides.
3x=-14
Subtract 4 from -10 to get -14.
x=\frac{-14}{3}
Divide both sides by 3.
x=-\frac{14}{3}
Fraction \frac{-14}{3} can be rewritten as -\frac{14}{3} by extracting the negative sign.
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