Distribute the nine on the left side through both terms of the binomial.

$\displaystyle 9(2-3x) = 18-27x$

Evaluate the right side of the equation.

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

Set the two simplified terms equal.

$\displaystyle 18-27x=3x-9$

Add $\displaystyle 27x$ on both sides.

$\displaystyle 18-27x+27x=3x-9+27x$

$\displaystyle 18=30x-9$

Add 9 on both sides.

$\displaystyle 18+9=30x-9+9$

$\displaystyle 27=30x$

Divide by thirty on both sides.

$\displaystyle \frac{27}{30}=\frac{30x}{30}$

Reduce both fractions.

The answer is:  $\displaystyle \frac{9}{10}$

Subtract 18 from both sides.

$\displaystyle -8x+18-18=46-18$

Simplify the equation.

$\displaystyle -8x = 28$

Divide by negative eight on both sides.

$\displaystyle \frac{-8x }{-8}= \frac{28}{-8}$

Reduce both fractions.

The answer is:  $\displaystyle -\frac{7}{2}$

Distribute the negative two on the right side.

The equation becomes:

$\displaystyle 6-9x= -8+14x$

Add $\displaystyle 9x$ on both sides.

$\displaystyle 6-9x+9x= -8+14x+9x$

$\displaystyle 6=23x-8$

Add 8 on both sides.

$\displaystyle 6+8=23x-8+8$

$\displaystyle 14= 23x$

Divide by 23 on both sides.

$\displaystyle \frac{14}{23}=\frac{ 23x}{23}$

The answer is:  $\displaystyle \frac{14}{23}$

Distribute the negative eight through the binomial.

$\displaystyle -8(3x)+(-8)(5)=-14+2x$

Simplify the left side.

$\displaystyle -24x-40 = -14+2x$

Add $\displaystyle 24x$ on both sides.

$\displaystyle -24x-40+24x = -14+2x+24x$

Simplify both sides.

$\displaystyle -40 =-14+26x$

Add 14 on both sides.

$\displaystyle -40 +14=-14+26x+14$

Simplify both sides.

$\displaystyle -26=26x$

Divide by 26 on both sides

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

The answer is:  $\displaystyle -1$

Multiply the negative eight through both terms of the binomial.

$\displaystyle -8(2x)-(-8)(3) = \frac{1}{5}$

Simplify the equation.

$\displaystyle -16x+24 = \frac{1}{5}$

Multiply by five on both sides to eliminate the fraction on the right side.

$\displaystyle 5(-16x+24 )= \frac{1}{5} \cdot 5$

$\displaystyle -80x+120 = 1$

Subtract 120 on both sides.

$\displaystyle -80x=-119$

Divide by negative 80 on both sides.  The double negatives will negate.

The answer is: $\displaystyle \frac{119}{80}$

Add 34 on both sides of the equation.

$\displaystyle 8x-34 +34= -13+34$

The equation becomes:

$\displaystyle 8x=21$

Divide by eight on both sides.

$\displaystyle \frac{8x}{8}=\frac{21}{8}$

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

Add $\displaystyle 4x$ on both sides.

$\displaystyle 5x-7+4x = 35-4x+4x$

Combine like terms.  The equation will become:  

$\displaystyle 9x-7 = 35$

Add seven on both sides.

$\displaystyle 9x-7+7 = 35+7$

$\displaystyle 9x=42$

Divide by nine on both sides.

$\displaystyle \frac{9x}{9}=\frac{42}{9}$

Reduce the fraction.

The answer is:  $\displaystyle \frac{14}{3}$

In order to eliminate the complications of converting fractions, we can multiply both sides by the least common denominator.

Write out the multiples of the denominators.

$\displaystyle 15-[15,30,45,60]$

$\displaystyle 20-[20,40,60]$

$\displaystyle 30-[30,60]$

Multiply both sides of the equation by 60.

$\displaystyle 60(\frac{1}{20}x+\frac{2}{15})= 60(\frac{1}{30})$

Simplify both sides.

$\displaystyle 3x+8 = 2$

Subtract eight from both sides.

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

$\displaystyle 3x=-6$

Divide by three on both sides.

$\displaystyle \frac{3x}{3}=\frac{-6}{3}$

Simplify both sides.

The answer is:  $\displaystyle -2$

Use distribution to simplify the right side.

$\displaystyle -8x = -8(-x)+(-8)(3)$

Simplify the parentheses.

$\displaystyle -8x =8x-24$

Subtract $\displaystyle 8x$ on both sides.

$\displaystyle -8x -8x=8x-24-8x$

$\displaystyle -16x = -24$

Divide by negative 16 on both sides.

$\displaystyle \frac{-16x }{-16}= \frac{-24}{-16}$

Reduce both fractions.

The answer is:  $\displaystyle \frac{3}{2}$

In order to eliminate the fractions, we can multiply both sides by the least common denominator.

The least common denominator can be determined by multiplying the two denominators together.

$\displaystyle 5\times 3 = 15$

$\displaystyle (15)(\frac{x}{5}+\frac{5}{3}) = 5(15)$

The equation becomes:

$\displaystyle 3x+25 = 75$

Subtract both sides by 25.

$\displaystyle 3x+25 -25= 75-25$

$\displaystyle 3x=50$

Divide by three on both sides.

$\displaystyle \frac{3x}{3}=\frac{50}{3}$

The answer is:  $\displaystyle \frac{50}{3}$