Solve 3+2x/4-x-4/6=5-x/18-1

$$\frac { 3 + 2 x } { 4 } - \frac { x - 4 } { 6 } = \frac { 5 - x } { 18 } - 1$$

Solve for x

$$x = -\frac{11}{2} = -5\frac{1}{2} = -5.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 4,6,18.

$$9\left(3+2x\right)-6\left(x-4\right)=2\left(5-x\right)-36$$

Use the distributive property to multiply 9 by 3+2x.

$$27+18x-6\left(x-4\right)=2\left(5-x\right)-36$$

Use the distributive property to multiply -6 by x-4.

$$27+18x-6x+24=2\left(5-x\right)-36$$

Combine 18x and -6x to get 12x.

$$27+12x+24=2\left(5-x\right)-36$$

Add 27 and 24 to get 51.

$$51+12x=2\left(5-x\right)-36$$

Use the distributive property to multiply 2 by 5-x.

$$51+12x=10-2x-36$$

Subtract 36 from 10 to get -26.

$$51+12x=-26-2x$$

Add 2x to both sides.

$$51+12x+2x=-26$$

Combine 12x and 2x to get 14x.

$$51+14x=-26$$

Subtract 51 from both sides.

$$14x=-26-51$$

Subtract 51 from -26 to get -77.

$$14x=-77$$

Divide both sides by 14.

$$x=\frac{-77}{14}$$

Reduce the fraction \frac{-77}{14} to lowest terms by extracting and canceling out 7.

$$x=-\frac{11}{2}$$