Solve 3x-1/2/4=2x-1/2-frac{1/3x}{3}

$$\frac { 3 x - \frac { 1 } { 2 } } { 4 } = 2 x - \frac { \frac { 1 } { 2 } - \frac { 1 } { 3 } x } { 3 }$$

Solve for x

$$x=\frac{3}{98}\approx 0.030612245$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$3\left(3x-\frac{1}{2}\right)=24x-4\left(\frac{1}{2}-\frac{1}{3}x\right)$$

Use the distributive property to multiply 3 by 3x-\frac{1}{2}.

$$9x+3\left(-\frac{1}{2}\right)=24x-4\left(\frac{1}{2}-\frac{1}{3}x\right)$$

Express 3\left(-\frac{1}{2}\right) as a single fraction.

$$9x+\frac{3\left(-1\right)}{2}=24x-4\left(\frac{1}{2}-\frac{1}{3}x\right)$$

Multiply 3 and -1 to get -3.

$$9x+\frac{-3}{2}=24x-4\left(\frac{1}{2}-\frac{1}{3}x\right)$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$9x-\frac{3}{2}=24x-4\left(\frac{1}{2}-\frac{1}{3}x\right)$$

Use the distributive property to multiply -4 by \frac{1}{2}-\frac{1}{3}x.

$$9x-\frac{3}{2}=24x-4\times \frac{1}{2}-4\left(-\frac{1}{3}\right)x$$

Multiply -4 and \frac{1}{2} to get \frac{-4}{2}.

$$9x-\frac{3}{2}=24x+\frac{-4}{2}-4\left(-\frac{1}{3}\right)x$$

Divide -4 by 2 to get -2.

$$9x-\frac{3}{2}=24x-2-4\left(-\frac{1}{3}\right)x$$

Express -4\left(-\frac{1}{3}\right) as a single fraction.

$$9x-\frac{3}{2}=24x-2+\frac{-4\left(-1\right)}{3}x$$

Multiply -4 and -1 to get 4.

$$9x-\frac{3}{2}=24x-2+\frac{4}{3}x$$

Combine 24x and \frac{4}{3}x to get \frac{76}{3}x.

$$9x-\frac{3}{2}=\frac{76}{3}x-2$$

Subtract \frac{76}{3}x from both sides.

$$9x-\frac{3}{2}-\frac{76}{3}x=-2$$

Combine 9x and -\frac{76}{3}x to get -\frac{49}{3}x.

$$-\frac{49}{3}x-\frac{3}{2}=-2$$

Add \frac{3}{2} to both sides.

$$-\frac{49}{3}x=-2+\frac{3}{2}$$

Convert -2 to fraction -\frac{4}{2}.

$$-\frac{49}{3}x=-\frac{4}{2}+\frac{3}{2}$$

Since -\frac{4}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$-\frac{49}{3}x=\frac{-4+3}{2}$$

Add -4 and 3 to get -1.

$$-\frac{49}{3}x=-\frac{1}{2}$$

Multiply both sides by -\frac{3}{49}, the reciprocal of -\frac{49}{3}.

$$x=-\frac{1}{2}\left(-\frac{3}{49}\right)$$

Multiply -\frac{1}{2} times -\frac{3}{49} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-\left(-3\right)}{2\times 49}$$

Do the multiplications in the fraction \frac{-\left(-3\right)}{2\times 49}.

$$x=\frac{3}{98}$$