Use distribution to simplify the right side.

$\displaystyle 81-2x = 9(x)+9(2)$

$\displaystyle 81-2x = 9x+18$

Add $\displaystyle 2x$ on both sides.

$\displaystyle 81-2x +2x= 9x+18+2x$

$\displaystyle 81= 11x+18$

Subtract 18 from both sides.

$\displaystyle 81-18= 11x+18-18$

$\displaystyle 63= 11x$

Divide by 11 on both sides.

$\displaystyle \frac{63}{11}= \frac{11x}{11}$

The answer is:  $\displaystyle \frac{63}{11}$

In order to solve for the x-variable, we will need use the elimination method to cancel the y-terms.

Multiply the first equation by three, so that we can use addition to turn two equations into one.

$\displaystyle \begin{Bmatrix} x-3y= 8\\x+9y=7 \end{Bmatrix} \rightarrow\begin{Bmatrix} 3[x-3y= 8]\\x+9y=7 \end{Bmatrix}\rightarrow \begin{Bmatrix} 3x-9y= 24\\x+9y=7 \end{Bmatrix}$

Adding the converted equations together will cancel out the $\displaystyle 9y$ terms, and will leave the x-variable by themselves.  The two equations will become one equation after adding.

$\displaystyle 4x=31$

Divide by four on both sides.

The answer is:  $\displaystyle \frac{31}{4}$

Distribute the nine through the binomial.

$\displaystyle 9(-x)+9(9)= -34$

Simplify the terms.

$\displaystyle -9x+81 = -34$

Subtract 81 from both sides.

$\displaystyle -9x+81 -81= -34-81$

$\displaystyle -9x= -115$

Divide by negative nine on both sides.  The negatives will cancel.

The answer is:  $\displaystyle \frac{115}{9}$

Simplify the right side by distributing the negative sign through the binomial.

$\displaystyle -8x-24=-2+9x$

Subtract $\displaystyle 9x$ from both sides.

$\displaystyle -8x-24-9x=-2+9x-9x$

$\displaystyle -17x-24=-2$

Add 24 on both sides.

$\displaystyle -17x-24+24=-2+24$

$\displaystyle -17x = 22$

Divide by negative 17 on both sides.

The answer is:  $\displaystyle -\frac{22}{17}$

Add $\displaystyle 8x$ on both sides.

$\displaystyle 8x-3+8x= 7-8x+8x$

Simplify both sides.

$\displaystyle 16x-3 =7$

Add three on both sides.

$\displaystyle 16x-3+3 =7+3$

$\displaystyle 16x=10$

Divide both sides by 16.

$\displaystyle \frac{16x}{16}=\frac{10}{16}$

Simplify both sides.

The answer is:  $\displaystyle \frac{5}{8}$

Subtract $\displaystyle 3x$ from both sides.

$\displaystyle -9x+18 -3x= -32+3x-3x$

$\displaystyle -12x+18 = -32$

Subtract 18 from both sides.

$\displaystyle -12x+18 -18= -32-18$

$\displaystyle -12x =-50$

Divide by negative 12 on both sides.

$\displaystyle \frac{-12x}{-12} =\frac{-50}{-12}$

Reduce the fractions.

The answer is:  $\displaystyle \frac{25}{6}$

Add three on both sides.

$\displaystyle \frac{1}{2x}-3+3 = 9+3$

$\displaystyle \frac{1}{2x}=12$

Multiply by $\displaystyle 2x$ on both sides.

$\displaystyle \frac{1}{2x}\cdot 2x=12\cdot2x$

$\displaystyle 1=24x$

Divide by 24 on both sides.

$\displaystyle \frac{1}{24}=\frac{24x}{24}$

The answer is:  $\displaystyle \frac{1}{24}$

Divide by three on both sides.

$\displaystyle \frac{3(x-9)}{3}=\frac{-63}{3}$

The equation becomes:  

$\displaystyle x-9 =-21$

Add nine on both sides.

$\displaystyle x-9 +9=-21+9$

$\displaystyle x=-12$

The answer is:  $\displaystyle -12$

Use distribution to expand the left side of the equation.

$\displaystyle -9(x)-(-9)(3)=6-x$

$\displaystyle -9x+27 = 6-x$

Add $\displaystyle 9x$ on both sides.

$\displaystyle -9x+27 +9x= 6-x+9x$

$\displaystyle 27=6+8x$

Subtract six from both sides.

$\displaystyle 27-6=6+8x-6$

$\displaystyle 21=8x$

Divide by eight on both sides.

The answer is:  $\displaystyle \frac{21}{8}$

Subtract $\displaystyle 3x$ on both sides.

$\displaystyle 8x-9 -3x= 3x-2-3x$

$\displaystyle 5x-9=-2$

Add nine on both sides.

$\displaystyle 5x-9+9=-2+9$

$\displaystyle 5x=7$

Divide by five on both sides.

$\displaystyle \frac{5x}{5}=\frac{7}{5}$

The answer is:  $\displaystyle \frac{7}{5}$