Solve 3x+8/10-9x-9/14=31x-4/14+4x-1/35

$$\frac{ 3x+8 }{ 10 } - \frac{ 9x-9 }{ 14 } = \frac{ 31x-4 }{ 14 } + \frac{ 4x-1 }{ 35 }$$

Solve for x

$$x=\frac{123}{187}\approx 0.657754011$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 70, the least common multiple of 10,14,35.

$$7\left(3x+8\right)-5\left(9x-9\right)=5\left(31x-4\right)+2\left(4x-1\right)$$

Use the distributive property to multiply 7 by 3x+8.

$$21x+56-5\left(9x-9\right)=5\left(31x-4\right)+2\left(4x-1\right)$$

Use the distributive property to multiply -5 by 9x-9.

$$21x+56-45x+45=5\left(31x-4\right)+2\left(4x-1\right)$$

Combine 21x and -45x to get -24x.

$$-24x+56+45=5\left(31x-4\right)+2\left(4x-1\right)$$

Add 56 and 45 to get 101.

$$-24x+101=5\left(31x-4\right)+2\left(4x-1\right)$$

Use the distributive property to multiply 5 by 31x-4.

$$-24x+101=155x-20+2\left(4x-1\right)$$

Use the distributive property to multiply 2 by 4x-1.

$$-24x+101=155x-20+8x-2$$

Combine 155x and 8x to get 163x.

$$-24x+101=163x-20-2$$

Subtract 2 from -20 to get -22.

$$-24x+101=163x-22$$

Subtract 163x from both sides.

$$-24x+101-163x=-22$$

Combine -24x and -163x to get -187x.

$$-187x+101=-22$$

Subtract 101 from both sides.

$$-187x=-22-101$$

Subtract 101 from -22 to get -123.

$$-187x=-123$$

Divide both sides by -187.

$$x=\frac{-123}{-187}$$

Fraction \frac{-123}{-187} can be simplified to \frac{123}{187} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{123}{187}$$