Add four on both sides to bring the four to the right side of the equation.

$\displaystyle 6x-4+4=10+4$

Simplify both sides.

$\displaystyle 6x=14$

Divide both sides by six.  

$\displaystyle x=\frac{14}{6}$

This fraction is not reduced.  Reduce the fraction by writing out the factors.

$\displaystyle x=\frac{14}{6} =\frac{2\times 7}{2 \times 3}$

Cancel out or divide the twos.

The answer is:  $\displaystyle \frac{7}{3}$

Subtract three from both sides.

$\displaystyle 5x+3-3 = -18-3$

Simplify.

$\displaystyle 5x=-21$

Divide by five on both sides.

$\displaystyle \frac{5x}{5}=\frac{-21}{5}$

Simplify both sides of the equation.

$\displaystyle x=-\frac{21}{5}$

The answer is:  $\displaystyle -\frac{21}{5}$

Solve the following equation for $\displaystyle r$

$\displaystyle 34r+17=85$

Let's begin by subtracting $\displaystyle 17$ from both sides. This will leave us with just $\displaystyle 34r$ on the left.

$\displaystyle 34r=85-17$

$\displaystyle 34r=68$

Next, let's divide both sides by $\displaystyle 34$ to get our answer:

$\displaystyle r=\frac{68}{34}=2$

So our answer is $\displaystyle 2$

To solve for x, we want to get x to be by itself or to stand alone.  Given the equation

$\displaystyle 2x - 4 = 8$

we will first add 4 to both sides.

$\displaystyle 2x - 4 + 4 = 8 + 4$

$\displaystyle 2x = 12$

Now, we will divide both sides by 2.

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

$\displaystyle x = 6$

$\displaystyle 2x+19=37$ Subtract $\displaystyle 19$ on both sides.

$\displaystyle 2x=18$ Divide $\displaystyle 2$ on both sides.

$\displaystyle x=9$

$\displaystyle 5x+76=46$ Subtract $\displaystyle 76$ on both sides. Since $\displaystyle 76$ is greater than $\displaystyle 46$ and is negative, our answer is negative. We treat as a normal subtraction.

$\displaystyle 5x=-30$ Divide $\displaystyle 5$ on both sides. When dividing with a negative answer, our answer is negative.

$\displaystyle x=-6$

$\displaystyle \frac{3x}{4}+47=95$ Subtract $\displaystyle 47$ on both sides.

$\displaystyle \frac{3x}{4}=48$ Multiply both sides by $\displaystyle \frac{4}{3}$.

$\displaystyle x=64$

$\displaystyle 4x-18=102$ Add $\displaystyle 18$ on both sides.

$\displaystyle 4x=120$ Divide $\displaystyle 4$ on both sides.

$\displaystyle x=30$

$\displaystyle 9x-125=-17$ Add $\displaystyle 125$ on both sides. Since $\displaystyle 125$ is greater than $\displaystyle 17$ and is positive, our answer is positive. We treat as a normal subtraction.

$\displaystyle 9x=108$ Divide $\displaystyle 9$ on both sides.

$\displaystyle x=12$

$\displaystyle \frac{5x}{7}-46=19$ Add $\displaystyle 46$ on both sides.

$\displaystyle \frac{5x}{7}=65$ Multiply $\displaystyle \frac{7}{5}$ on both sides.

$\displaystyle x=91$