Solve 6(x+1)-4(2x+3)=7(x-1)+5(9-x)

$$6 ( x + 1 ) - 4 ( 2 x + 3 ) = 7 ( x - 1 ) + 5 ( 9 - x )$$

Solve for x

$$x=-11$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by x+1.

$$6x+6-4\left(2x+3\right)=7\left(x-1\right)+5\left(9-x\right)$$

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

$$6x+6-8x-12=7\left(x-1\right)+5\left(9-x\right)$$

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

$$-2x+6-12=7\left(x-1\right)+5\left(9-x\right)$$

Subtract 12 from 6 to get -6.

$$-2x-6=7\left(x-1\right)+5\left(9-x\right)$$

Use the distributive property to multiply 7 by x-1.

$$-2x-6=7x-7+5\left(9-x\right)$$

Use the distributive property to multiply 5 by 9-x.

$$-2x-6=7x-7+45-5x$$

Add -7 and 45 to get 38.

$$-2x-6=7x+38-5x$$

Combine 7x and -5x to get 2x.

$$-2x-6=2x+38$$

Subtract 2x from both sides.

$$-2x-6-2x=38$$

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

$$-4x-6=38$$

Add 6 to both sides.

$$-4x=38+6$$

Add 38 and 6 to get 44.

$$-4x=44$$

Divide both sides by -4.

$$x=\frac{44}{-4}$$

Divide 44 by -4 to get -11.

$$x=-11$$