Solve 3x-17/8-1+4x/3=1-x/4-9+x/6

$$\frac{ 3x-17 }{ 8 } - \frac{ 1+4x }{ 3 } = \frac{ 1-x }{ 4 } - \frac{ 9+x }{ 6 }$$

Solve for x

$$x = -\frac{29}{13} = -2\frac{3}{13} \approx -2.230769231$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 8,3,4,6.

$$3\left(3x-17\right)-8\left(1+4x\right)=6\left(1-x\right)-4\left(9+x\right)$$

Use the distributive property to multiply 3 by 3x-17.

$$9x-51-8\left(1+4x\right)=6\left(1-x\right)-4\left(9+x\right)$$

Use the distributive property to multiply -8 by 1+4x.

$$9x-51-8-32x=6\left(1-x\right)-4\left(9+x\right)$$

Subtract 8 from -51 to get -59.

$$9x-59-32x=6\left(1-x\right)-4\left(9+x\right)$$

Combine 9x and -32x to get -23x.

$$-23x-59=6\left(1-x\right)-4\left(9+x\right)$$

Use the distributive property to multiply 6 by 1-x.

$$-23x-59=6-6x-4\left(9+x\right)$$

Use the distributive property to multiply -4 by 9+x.

$$-23x-59=6-6x-36-4x$$

Subtract 36 from 6 to get -30.

$$-23x-59=-30-6x-4x$$

Combine -6x and -4x to get -10x.

$$-23x-59=-30-10x$$

Add 10x to both sides.

$$-23x-59+10x=-30$$

Combine -23x and 10x to get -13x.

$$-13x-59=-30$$

Add 59 to both sides.

$$-13x=-30+59$$

Add -30 and 59 to get 29.

$$-13x=29$$

Divide both sides by -13.

$$x=\frac{29}{-13}$$

Fraction \frac{29}{-13} can be rewritten as -\frac{29}{13} by extracting the negative sign.

$$x=-\frac{29}{13}$$