Solve (x+8)(2-x)/2=3(1-2x)-(2x+3)(x-7)/4+(-x+1)/4

$$\frac { ( x + 8 ) ( 2 - x ) } { 2 } = 3 ( 1 - 2 x ) - \frac { ( 2 x + 3 ) ( x - 7 ) } { 4 } + \frac { ( - x + 1 ) } { 4 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(x+8\right)\left(2-x\right)=12\left(1-2x\right)-\left(2x+3\right)\left(x-7\right)-x+1$$

Use the distributive property to multiply 2 by x+8.

$$\left(2x+16\right)\left(2-x\right)=12\left(1-2x\right)-\left(2x+3\right)\left(x-7\right)-x+1$$

Use the distributive property to multiply 2x+16 by 2-x and combine like terms.

$$-12x-2x^{2}+32=12\left(1-2x\right)-\left(2x+3\right)\left(x-7\right)-x+1$$

Use the distributive property to multiply 12 by 1-2x.

$$-12x-2x^{2}+32=12-24x-\left(2x+3\right)\left(x-7\right)-x+1$$

Use the distributive property to multiply 2x+3 by x-7 and combine like terms.

$$-12x-2x^{2}+32=12-24x-\left(2x^{2}-11x-21\right)-x+1$$

To find the opposite of 2x^{2}-11x-21, find the opposite of each term.

$$-12x-2x^{2}+32=12-24x-2x^{2}+11x+21-x+1$$

Combine -24x and 11x to get -13x.

$$-12x-2x^{2}+32=12-13x-2x^{2}+21-x+1$$

Add 12 and 21 to get 33.

$$-12x-2x^{2}+32=33-13x-2x^{2}-x+1$$

Add 33 and 1 to get 34.

$$-12x-2x^{2}+32=34-13x-2x^{2}-x$$

Add 13x to both sides.

$$-12x-2x^{2}+32+13x=34-2x^{2}-x$$

Combine -12x and 13x to get x.

$$x-2x^{2}+32=34-2x^{2}-x$$

Add 2x^{2} to both sides.

$$x-2x^{2}+32+2x^{2}=34-x$$

Combine -2x^{2} and 2x^{2} to get 0.

$$x+32=34-x$$

Add x to both sides.

$$x+32+x=34$$

Combine x and x to get 2x.

$$2x+32=34$$

Subtract 32 from both sides.

$$2x=34-32$$

Subtract 32 from 34 to get 2.

$$2x=2$$

Divide both sides by 2.

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

Divide 2 by 2 to get 1.

$$x=1$$