Solve 4x+1/3=5(3x+2)/4-2(x+1)/3

$$\frac { 4 x + 1 } { 3 } = \frac { 5 ( 3 x + 2 ) } { 4 } - \frac { 2 ( x + 1 ) } { 3 }$$

Solve for x

$$x=-\frac{6}{7}\approx -0.857142857$$

Steps for Solving Linear Equation

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

$$4\left(4x+1\right)=3\times 5\left(3x+2\right)-4\times 2\left(x+1\right)$$

Use the distributive property to multiply 4 by 4x+1.

$$16x+4=3\times 5\left(3x+2\right)-4\times 2\left(x+1\right)$$

Multiply 3 and 5 to get 15. Multiply -4 and 2 to get -8.

$$16x+4=15\left(3x+2\right)-8\left(x+1\right)$$

Use the distributive property to multiply 15 by 3x+2.

$$16x+4=45x+30-8\left(x+1\right)$$

Use the distributive property to multiply -8 by x+1.

$$16x+4=45x+30-8x-8$$

Combine 45x and -8x to get 37x.

$$16x+4=37x+30-8$$

Subtract 8 from 30 to get 22.

$$16x+4=37x+22$$

Subtract 37x from both sides.

$$16x+4-37x=22$$

Combine 16x and -37x to get -21x.

$$-21x+4=22$$

Subtract 4 from both sides.

$$-21x=22-4$$

Subtract 4 from 22 to get 18.

$$-21x=18$$

Divide both sides by -21.

$$x=\frac{18}{-21}$$

Reduce the fraction \frac{18}{-21} to lowest terms by extracting and canceling out 3.

$$x=-\frac{6}{7}$$