Solve 129x+1/9+5-x/4=1-38+2/6

$$1 \frac { 29 x + 1 } { 9 } + \frac { 5 - x } { 4 } = 1 - \frac { 38 + 2 } { 6 }$$

Solve for x

$$x = -\frac{253}{107} = -2\frac{39}{107} \approx -2.364485981$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 9,4,6.

$$4\left(29x+1\right)+9\left(5-x\right)=36-6\left(38+2\right)$$

Use the distributive property to multiply 4 by 29x+1.

$$116x+4+9\left(5-x\right)=36-6\left(38+2\right)$$

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

$$116x+4+45-9x=36-6\left(38+2\right)$$

Add 4 and 45 to get 49.

$$116x+49-9x=36-6\left(38+2\right)$$

Combine 116x and -9x to get 107x.

$$107x+49=36-6\left(38+2\right)$$

Add 38 and 2 to get 40.

$$107x+49=36-6\times 40$$

Multiply -6 and 40 to get -240.

$$107x+49=36-240$$

Subtract 240 from 36 to get -204.

$$107x+49=-204$$

Subtract 49 from both sides.

$$107x=-204-49$$

Subtract 49 from -204 to get -253.

$$107x=-253$$

Divide both sides by 107.

$$x=\frac{-253}{107}$$

Fraction \frac{-253}{107} can be rewritten as -\frac{253}{107} by extracting the negative sign.

$$x=-\frac{253}{107}$$