Solve 2(3x-4y)+5=3(2y+3x+2)

$$2 ( 3 x - 4 y ) + 5 = 3 ( 2 y + 3 x + 2 )$$

Solve for x

$$x=\frac{-14y-1}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 3x-4y.

$$6x-8y+5=3\left(2y+3x+2\right)$$

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

$$6x-8y+5=6y+9x+6$$

Subtract 9x from both sides.

$$6x-8y+5-9x=6y+6$$

Combine 6x and -9x to get -3x.

$$-3x-8y+5=6y+6$$

Add 8y to both sides.

$$-3x+5=6y+6+8y$$

Combine 6y and 8y to get 14y.

$$-3x+5=14y+6$$

Subtract 5 from both sides.

$$-3x=14y+6-5$$

Subtract 5 from 6 to get 1.

$$-3x=14y+1$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{14y+1}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{14y+1}{-3}$$

Divide 14y+1 by -3.

$$x=\frac{-14y-1}{3}$$

Solve for y

$$y=\frac{-3x-1}{14}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 3x-4y.

$$6x-8y+5=3\left(2y+3x+2\right)$$

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

$$6x-8y+5=6y+9x+6$$

Subtract 6y from both sides.

$$6x-8y+5-6y=9x+6$$

Combine -8y and -6y to get -14y.

$$6x-14y+5=9x+6$$

Subtract 6x from both sides.

$$-14y+5=9x+6-6x$$

Combine 9x and -6x to get 3x.

$$-14y+5=3x+6$$

Subtract 5 from both sides.

$$-14y=3x+6-5$$

Subtract 5 from 6 to get 1.

$$-14y=3x+1$$

Divide both sides by -14.

$$\frac{-14y}{-14}=\frac{3x+1}{-14}$$

Dividing by -14 undoes the multiplication by -14.

$$y=\frac{3x+1}{-14}$$

Divide 3x+1 by -14.

$$y=\frac{-3x-1}{14}$$