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

$$2 \cdot ( 3 x + 4 ) - 2 \cdot ( 5 x + 2 ) = 3 \cdot ( 2 x + 2 ) + 4 \cdot ( 4 x + 4 )$$

Solve for x

$$x=-\frac{9}{13}\approx -0.692307692$$

Steps for Solving Linear Equation

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

$$6x+8-2\left(5x+2\right)=3\left(2x+2\right)+4\left(4x+4\right)$$

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

$$6x+8-10x-4=3\left(2x+2\right)+4\left(4x+4\right)$$

Combine 6x and -10x to get -4x.

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

Subtract 4 from 8 to get 4.

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

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

$$-4x+4=6x+6+4\left(4x+4\right)$$

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

$$-4x+4=6x+6+16x+16$$

Combine 6x and 16x to get 22x.

$$-4x+4=22x+6+16$$

Add 6 and 16 to get 22.

$$-4x+4=22x+22$$

Subtract 22x from both sides.

$$-4x+4-22x=22$$

Combine -4x and -22x to get -26x.

$$-26x+4=22$$

Subtract 4 from both sides.

$$-26x=22-4$$

Subtract 4 from 22 to get 18.

$$-26x=18$$

Divide both sides by -26.

$$x=\frac{18}{-26}$$

Reduce the fraction \frac{18}{-26} to lowest terms by extracting and canceling out 2.

$$x=-\frac{9}{13}$$