Solve 5a(x+2)+3(x+a)=4(x+3a)-5(1-ax)

$$5 a ( x + 2 ) + 3 ( x + a ) = 4 ( x + 3 a ) - 5 ( 1 - a x )$$

Solve for a

$$a=x-5$$

Solution Steps

Use the distributive property to multiply 5a by x+2.

$$5ax+10a+3\left(x+a\right)=4\left(x+3a\right)-5\left(1-ax\right)$$

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

$$5ax+10a+3x+3a=4\left(x+3a\right)-5\left(1-ax\right)$$

Combine 10a and 3a to get 13a.

$$5ax+13a+3x=4\left(x+3a\right)-5\left(1-ax\right)$$

Use the distributive property to multiply 4 by x+3a.

$$5ax+13a+3x=4x+12a-5\left(1-ax\right)$$

Use the distributive property to multiply -5 by 1-ax.

$$5ax+13a+3x=4x+12a-5+5ax$$

Subtract 12a from both sides.

$$5ax+13a+3x-12a=4x-5+5ax$$

Combine 13a and -12a to get a.

$$5ax+a+3x=4x-5+5ax$$

Subtract 5ax from both sides.

$$5ax+a+3x-5ax=4x-5$$

Combine 5ax and -5ax to get 0.

$$a+3x=4x-5$$

Subtract 3x from both sides.

$$a=4x-5-3x$$

Combine 4x and -3x to get x.

$$a=x-5$$

Solve for x

$$x=a+5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5a by x+2.

$$5ax+10a+3\left(x+a\right)=4\left(x+3a\right)-5\left(1-ax\right)$$

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

$$5ax+10a+3x+3a=4\left(x+3a\right)-5\left(1-ax\right)$$

Combine 10a and 3a to get 13a.

$$5ax+13a+3x=4\left(x+3a\right)-5\left(1-ax\right)$$

Use the distributive property to multiply 4 by x+3a.

$$5ax+13a+3x=4x+12a-5\left(1-ax\right)$$

Use the distributive property to multiply -5 by 1-ax.

$$5ax+13a+3x=4x+12a-5+5xa$$

Subtract 4x from both sides.

$$5ax+13a+3x-4x=12a-5+5xa$$

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

$$5ax+13a-x=12a-5+5xa$$

Subtract 5xa from both sides.

$$5ax+13a-x-5xa=12a-5$$

Combine 5ax and -5xa to get 0.

$$13a-x=12a-5$$

Subtract 13a from both sides.

$$-x=12a-5-13a$$

Combine 12a and -13a to get -a.

$$-x=-a-5$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{-a-5}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{-a-5}{-1}$$

Divide -a-5 by -1.

$$x=a+5$$