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.

\(\displaystyle x=91\)