Solve 4(5x-2)/3-6(3x+2)/7=42-5(7x-4)/4

$$\frac { 4 ( 5 x - 2 ) } { 3 } - \frac { 6 ( 3 x + 2 ) } { 7 } = 42 - \frac { 5 ( 7 x - 4 ) } { 4 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 84, the least common multiple of 3,7,4.

$$28\times 4\left(5x-2\right)-12\times 6\left(3x+2\right)=3528-21\times 5\left(7x-4\right)$$

Multiply 28 and 4 to get 112.

$$112\left(5x-2\right)-12\times 6\left(3x+2\right)=3528-21\times 5\left(7x-4\right)$$

Use the distributive property to multiply 112 by 5x-2.

$$560x-224-12\times 6\left(3x+2\right)=3528-21\times 5\left(7x-4\right)$$

Multiply -12 and 6 to get -72.

$$560x-224-72\left(3x+2\right)=3528-21\times 5\left(7x-4\right)$$

Use the distributive property to multiply -72 by 3x+2.

$$560x-224-216x-144=3528-21\times 5\left(7x-4\right)$$

Combine 560x and -216x to get 344x.

$$344x-224-144=3528-21\times 5\left(7x-4\right)$$

Subtract 144 from -224 to get -368.

$$344x-368=3528-21\times 5\left(7x-4\right)$$

Multiply -21 and 5 to get -105.

$$344x-368=3528-105\left(7x-4\right)$$

Use the distributive property to multiply -105 by 7x-4.

$$344x-368=3528-735x+420$$

Add 3528 and 420 to get 3948.

$$344x-368=3948-735x$$

Add 735x to both sides.

$$344x-368+735x=3948$$

Combine 344x and 735x to get 1079x.

$$1079x-368=3948$$

Add 368 to both sides.

$$1079x=3948+368$$

Add 3948 and 368 to get 4316.

$$1079x=4316$$

Divide both sides by 1079.

$$x=\frac{4316}{1079}$$

Divide 4316 by 1079 to get 4.

$$x=4$$