Solve 7/12x+10x-15/3-x=4(2x-1)/3-3(2-x)/4

$$\frac { 7 } { 12 } x + \frac { 10 x - 15 } { 3 } - x = \frac { 4 ( 2 x - 1 ) } { 3 } - \frac { 3 ( 2 - x ) } { 4 }$$

Solve for x

$$x = -\frac{13}{3} = -4\frac{1}{3} \approx -4.333333333$$

Steps for Solving Linear Equation

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

$$7x+4\left(10x-15\right)-12x=4\times 4\left(2x-1\right)-3\times 3\left(2-x\right)$$

Use the distributive property to multiply 4 by 10x-15.

$$7x+40x-60-12x=4\times 4\left(2x-1\right)-3\times 3\left(2-x\right)$$

Combine 7x and 40x to get 47x.

$$47x-60-12x=4\times 4\left(2x-1\right)-3\times 3\left(2-x\right)$$

Combine 47x and -12x to get 35x.

$$35x-60=4\times 4\left(2x-1\right)-3\times 3\left(2-x\right)$$

Multiply 4 and 4 to get 16. Multiply -3 and 3 to get -9.

$$35x-60=16\left(2x-1\right)-9\left(2-x\right)$$

Use the distributive property to multiply 16 by 2x-1.

$$35x-60=32x-16-9\left(2-x\right)$$

Use the distributive property to multiply -9 by 2-x.

$$35x-60=32x-16-18+9x$$

Subtract 18 from -16 to get -34.

$$35x-60=32x-34+9x$$

Combine 32x and 9x to get 41x.

$$35x-60=41x-34$$

Subtract 41x from both sides.

$$35x-60-41x=-34$$

Combine 35x and -41x to get -6x.

$$-6x-60=-34$$

Add 60 to both sides.

$$-6x=-34+60$$

Add -34 and 60 to get 26.

$$-6x=26$$

Divide both sides by -6.

$$x=\frac{26}{-6}$$

Reduce the fraction \frac{26}{-6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{13}{3}$$