Solve (3x-7/3)div(-4)-(x+3/2)div6=(7x-125/100)div3+(5x-1/6)div2

$$(3x- \frac{ 7 }{ 3 } ) \div (-4)-(x+ \frac{ 3 }{ 2 } ) \div 6=(7x- \frac{ 125 }{ 100 } ) \div 3+(5x- \frac{ 1 }{ 6 } ) \div 2$$

Solve for x

$$x=\frac{10}{69}\approx 0.144927536$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of -4,6,3,2.

$$-3\left(3x-\frac{7}{3}\right)-2\left(x+\frac{3}{2}\right)=4\left(7x-\frac{125}{100}\right)+6\left(5x-\frac{1}{6}\right)$$

Use the distributive property to multiply -3 by 3x-\frac{7}{3}.

$$-9x-3\left(-\frac{7}{3}\right)-2\left(x+\frac{3}{2}\right)=4\left(7x-\frac{125}{100}\right)+6\left(5x-\frac{1}{6}\right)$$

Multiply -3 times -\frac{7}{3}.

$$-9x+7-2\left(x+\frac{3}{2}\right)=4\left(7x-\frac{125}{100}\right)+6\left(5x-\frac{1}{6}\right)$$

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

$$-9x+7-2x-2\times \frac{3}{2}=4\left(7x-\frac{125}{100}\right)+6\left(5x-\frac{1}{6}\right)$$

Multiply -2 times \frac{3}{2}.

$$-9x+7-2x-3=4\left(7x-\frac{125}{100}\right)+6\left(5x-\frac{1}{6}\right)$$

Combine -9x and -2x to get -11x.

$$-11x+7-3=4\left(7x-\frac{125}{100}\right)+6\left(5x-\frac{1}{6}\right)$$

Subtract 3 from 7 to get 4.

$$-11x+4=4\left(7x-\frac{125}{100}\right)+6\left(5x-\frac{1}{6}\right)$$

Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$-11x+4=4\left(7x-\frac{5}{4}\right)+6\left(5x-\frac{1}{6}\right)$$

Use the distributive property to multiply 4 by 7x-\frac{5}{4}.

$$-11x+4=28x+4\left(-\frac{5}{4}\right)+6\left(5x-\frac{1}{6}\right)$$

Cancel out 4 and 4.

$$-11x+4=28x-5+6\left(5x-\frac{1}{6}\right)$$

Use the distributive property to multiply 6 by 5x-\frac{1}{6}.

$$-11x+4=28x-5+30x+6\left(-\frac{1}{6}\right)$$

Cancel out 6 and 6.

$$-11x+4=28x-5+30x-1$$

Combine 28x and 30x to get 58x.

$$-11x+4=58x-5-1$$

Subtract 1 from -5 to get -6.

$$-11x+4=58x-6$$

Subtract 58x from both sides.

$$-11x+4-58x=-6$$

Combine -11x and -58x to get -69x.

$$-69x+4=-6$$

Subtract 4 from both sides.

$$-69x=-6-4$$

Subtract 4 from -6 to get -10.

$$-69x=-10$$

Divide both sides by -69.

$$x=\frac{-10}{-69}$$

Fraction \frac{-10}{-69} can be simplified to \frac{10}{69} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{10}{69}$$