Solve 6(x+9)-3(2x+1)+2x-9+6=9(x+7)+18(-x-1)+16

$$6 ( x + 9 ) - 3 ( 2 x + 1 ) + 2 x - 9 + 6 = 9 ( x + 7 ) + 18 ( - x - 1 ) + 16$$

Solve for x

$$x = \frac{13}{11} = 1\frac{2}{11} \approx 1.181818182$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by x+9.

$$6x+54-3\left(2x+1\right)+2x-9+6=9\left(x+7\right)+18\left(-x-1\right)+16$$

Use the distributive property to multiply -3 by 2x+1.

$$6x+54-6x-3+2x-9+6=9\left(x+7\right)+18\left(-x-1\right)+16$$

Combine 6x and -6x to get 0.

$$54-3+2x-9+6=9\left(x+7\right)+18\left(-x-1\right)+16$$

Subtract 3 from 54 to get 51.

$$51+2x-9+6=9\left(x+7\right)+18\left(-x-1\right)+16$$

Subtract 9 from 51 to get 42.

$$42+2x+6=9\left(x+7\right)+18\left(-x-1\right)+16$$

Add 42 and 6 to get 48.

$$48+2x=9\left(x+7\right)+18\left(-x-1\right)+16$$

Use the distributive property to multiply 9 by x+7.

$$48+2x=9x+63+18\left(-x-1\right)+16$$

Use the distributive property to multiply 18 by -x-1.

$$48+2x=9x+63+18\left(-x\right)-18+16$$

Subtract 18 from 63 to get 45.

$$48+2x=9x+45+18\left(-x\right)+16$$

Add 45 and 16 to get 61.

$$48+2x=9x+61+18\left(-x\right)$$

Subtract 9x from both sides.

$$48+2x-9x=61+18\left(-x\right)$$

Combine 2x and -9x to get -7x.

$$48-7x=61+18\left(-x\right)$$

Subtract 18\left(-x\right) from both sides.

$$48-7x-18\left(-x\right)=61$$

Multiply -1 and 18 to get -18.

$$48-7x-18\left(-1\right)x=61$$

Multiply -18 and -1 to get 18.

$$48-7x+18x=61$$

Combine -7x and 18x to get 11x.

$$48+11x=61$$

Subtract 48 from both sides.

$$11x=61-48$$

Subtract 48 from 61 to get 13.

$$11x=13$$

Divide both sides by 11.

$$x=\frac{13}{11}$$