Solve quad4(x-2)-3(2x+a)=2(2x-a)

$$\quad 4 ( x - 2 ) - 3 ( 2 x + a ) = 2 ( 2 x - a )$$

Solve for a

$$a=-6x-8$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by x-2.

$$4x-8-3\left(2x+a\right)=2\left(2x-a\right)$$

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

$$4x-8-6x-3a=2\left(2x-a\right)$$

Combine 4x and -6x to get -2x.

$$-2x-8-3a=2\left(2x-a\right)$$

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

$$-2x-8-3a=4x-2a$$

Add 2a to both sides.

$$-2x-8-3a+2a=4x$$

Combine -3a and 2a to get -a.

$$-2x-8-a=4x$$

Add 2x to both sides.

$$-8-a=4x+2x$$

Combine 4x and 2x to get 6x.

$$-8-a=6x$$

Add 8 to both sides.

$$-a=6x+8$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{6x+8}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{6x+8}{-1}$$

Divide 6x+8 by -1.

$$a=-6x-8$$

Solve for x

$$x=-\frac{a}{6}-\frac{4}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by x-2.

$$4x-8-3\left(2x+a\right)=2\left(2x-a\right)$$

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

$$4x-8-6x-3a=2\left(2x-a\right)$$

Combine 4x and -6x to get -2x.

$$-2x-8-3a=2\left(2x-a\right)$$

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

$$-2x-8-3a=4x-2a$$

Subtract 4x from both sides.

$$-2x-8-3a-4x=-2a$$

Combine -2x and -4x to get -6x.

$$-6x-8-3a=-2a$$

Add 8 to both sides.

$$-6x-3a=-2a+8$$

Add 3a to both sides.

$$-6x=-2a+8+3a$$

Combine -2a and 3a to get a.

$$-6x=a+8$$

Divide both sides by -6.

$$\frac{-6x}{-6}=\frac{a+8}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$x=\frac{a+8}{-6}$$

Divide a+8 by -6.

$$x=-\frac{a}{6}-\frac{4}{3}$$