Solve 5-x/2-3(x+5/2+1)=x-2/4-(7/2+x)

$$\frac { 5 - x } { 2 } - 3 ( \frac { x + 5 } { 2 } + 1 ) = \frac { x - 2 } { 4 } - ( \frac { 7 } { 2 } + x )$$

Solve for x

$$x = -\frac{16}{5} = -3\frac{1}{5} = -3.2$$

Steps for Solving Linear Equation

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

$$2\left(5-x\right)-12\left(\frac{x+5}{2}+1\right)=x-2-4\left(\frac{7}{2}+x\right)$$

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

$$10-2x-12\left(\frac{x+5}{2}+1\right)=x-2-4\left(\frac{7}{2}+x\right)$$

Use the distributive property to multiply -4 by \frac{7}{2}+x.

$$10-2x-12\left(\frac{x+5}{2}+1\right)=x-2-4\times \frac{7}{2}-4x$$

Express -4\times \frac{7}{2} as a single fraction.

$$10-2x-12\left(\frac{x+5}{2}+1\right)=x-2+\frac{-4\times 7}{2}-4x$$

Multiply -4 and 7 to get -28.

$$10-2x-12\left(\frac{x+5}{2}+1\right)=x-2+\frac{-28}{2}-4x$$

Divide -28 by 2 to get -14.

$$10-2x-12\left(\frac{x+5}{2}+1\right)=x-2-14-4x$$

Subtract 14 from -2 to get -16.

$$10-2x-12\left(\frac{x+5}{2}+1\right)=x-16-4x$$

Combine x and -4x to get -3x.

$$10-2x-12\left(\frac{x+5}{2}+1\right)=-3x-16$$

Divide each term of x+5 by 2 to get \frac{1}{2}x+\frac{5}{2}.

$$10-2x-12\left(\frac{1}{2}x+\frac{5}{2}+1\right)=-3x-16$$

Convert 1 to fraction \frac{2}{2}.

$$10-2x-12\left(\frac{1}{2}x+\frac{5}{2}+\frac{2}{2}\right)=-3x-16$$

Since \frac{5}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$10-2x-12\left(\frac{1}{2}x+\frac{5+2}{2}\right)=-3x-16$$

Add 5 and 2 to get 7.

$$10-2x-12\left(\frac{1}{2}x+\frac{7}{2}\right)=-3x-16$$

Use the distributive property to multiply -12 by \frac{1}{2}x+\frac{7}{2}.

$$10-2x-12\times \frac{1}{2}x-12\times \frac{7}{2}=-3x-16$$

Multiply -12 and \frac{1}{2} to get \frac{-12}{2}.

$$10-2x+\frac{-12}{2}x-12\times \frac{7}{2}=-3x-16$$

Divide -12 by 2 to get -6.

$$10-2x-6x-12\times \frac{7}{2}=-3x-16$$

Express -12\times \frac{7}{2} as a single fraction.

$$10-2x-6x+\frac{-12\times 7}{2}=-3x-16$$

Multiply -12 and 7 to get -84.

$$10-2x-6x+\frac{-84}{2}=-3x-16$$

Divide -84 by 2 to get -42.

$$10-2x-6x-42=-3x-16$$

Combine -2x and -6x to get -8x.

$$10-8x-42=-3x-16$$

Subtract 42 from 10 to get -32.

$$-32-8x=-3x-16$$

Add 3x to both sides.

$$-32-8x+3x=-16$$

Combine -8x and 3x to get -5x.

$$-32-5x=-16$$

Add 32 to both sides.

$$-5x=-16+32$$

Add -16 and 32 to get 16.

$$-5x=16$$

Divide both sides by -5.

$$x=\frac{16}{-5}$$

Fraction \frac{16}{-5} can be rewritten as -\frac{16}{5} by extracting the negative sign.

$$x=-\frac{16}{5}$$