Solve --x+2/7+3x+2/3=-x+6/14+5

$$- \frac { - x + 2 } { 7 } + \frac { 3 x + 2 } { 3 } = \frac { - x + 6 } { 14 } + 5$$

Solve for x

$$x = \frac{212}{51} = 4\frac{8}{51} \approx 4.156862745$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 42, the least common multiple of 7,3,14.

$$-6\left(-x+2\right)+14\left(3x+2\right)=3\left(-x+6\right)+210$$

Use the distributive property to multiply -6 by -x+2.

$$-6\left(-x\right)-12+14\left(3x+2\right)=3\left(-x+6\right)+210$$

Multiply -6 and -1 to get 6.

$$6x-12+14\left(3x+2\right)=3\left(-x+6\right)+210$$

Use the distributive property to multiply 14 by 3x+2.

$$6x-12+42x+28=3\left(-x+6\right)+210$$

Combine 6x and 42x to get 48x.

$$48x-12+28=3\left(-x+6\right)+210$$

Add -12 and 28 to get 16.

$$48x+16=3\left(-x+6\right)+210$$

Use the distributive property to multiply 3 by -x+6.

$$48x+16=3\left(-x\right)+18+210$$

Add 18 and 210 to get 228.

$$48x+16=3\left(-x\right)+228$$

Subtract 3\left(-x\right) from both sides.

$$48x+16-3\left(-x\right)=228$$

Multiply -1 and 3 to get -3.

$$48x+16-3\left(-1\right)x=228$$

Multiply -3 and -1 to get 3.

$$48x+16+3x=228$$

Combine 48x and 3x to get 51x.

$$51x+16=228$$

Subtract 16 from both sides.

$$51x=228-16$$

Subtract 16 from 228 to get 212.

$$51x=212$$

Divide both sides by 51.

$$x=\frac{212}{51}$$