In order to solve this equation, you have to isolate the variable to one side by reversing the operations done to it. Whatever is done on one side of the equals sign must be done on the other side of the equals sign as well. When the variable is by itself, it will be defined as whatever is left on the other side of the equals sign, and the equation is solved.

\(\displaystyle 4x+2=22\)

Subtract \(\displaystyle 2\) from each side.

\(\displaystyle 4x+2-2=22-2\)

\(\displaystyle 4x=22-2\)

\(\displaystyle 4x=20\)

Divide each side by \(\displaystyle 4\).

\(\displaystyle \frac{4x}{4}=\frac{20}{4}\)

\(\displaystyle x=\frac{20}{4}\)

\(\displaystyle x=5\)

In order to solve this equation, you have to isolate the variable to one side by reversing the operations done to it. Whatever is done on one side of the equals sign must be done on the other side of the equals sign as well. When the variable is by itself, it will be defined as whatever is left on the other side of the equals sign, and the equation is solved.

\(\displaystyle 3x-1=26\)

Add \(\displaystyle 1\) to both sides of the equation.

\(\displaystyle 3x-1+1=26+1\)

\(\displaystyle 3x=27\)

Divide each side by \(\displaystyle 3\).

\(\displaystyle \frac{3x}{3}=\frac{27}{3}\)

\(\displaystyle x=\frac{27}{3}\)

\(\displaystyle x=9\)

In order to solve this equation, you have to isolate the variable to one side by reversing the operations done to it. Whatever is done on one side of the equals sign must be done on the other side of the equals sign as well. When the variable is by itself, it will be defined as whatever is left on the other side of the equals sign, and the equation is solved.

\(\displaystyle x^2+2=18\)

Subtract \(\displaystyle 2\) from each side of the equation.

\(\displaystyle x^2+2-2=18-2\)

\(\displaystyle x^2=18-2\)

\(\displaystyle x^2=16\)

Take the square root of each side of the equation and solve for the unknown.

\(\displaystyle \sqrt{x^2}=\sqrt{16}\)

\(\displaystyle x=\sqrt{16}\)

\(\displaystyle x=\sqrt{4*4}\)

\(\displaystyle x=4\)

To "break" or remove the absolute value, we can create two different equations. 

We can say 

\(\displaystyle x-4=2\)

and 

\(\displaystyle x-4=-2\)

When we solve each of these equations, we get x= 6 and x=2.

Explanation:

The goal is to isolate the variable to one side.

\(\displaystyle 3x+5=11\)

Subtract \(\displaystyle 5\) from each side of the equation:

\(\displaystyle 3x+5-5=11-5\)

\(\displaystyle 3x=6\)

Divide each side by \(\displaystyle 3\):

\(\displaystyle \frac{3x}{3}=\frac{6}{3}\)

\(\displaystyle x=2\)

\(\displaystyle -3t+2=8\)

\(\displaystyle -3t+2-2=8-2\)

\(\displaystyle -3t=6\)

\(\displaystyle \frac{-3t}{-3}=\frac{6}{-3}\)

\(\displaystyle t=-2\)

\(\displaystyle 2x + 4 = 3x - 9\)

You must put your \(\displaystyle x\)'s and numbers on opposite sides of the equation. First, you subtract \(\displaystyle 2x\) from both sides of the equation:

\(\displaystyle 2x + 4 -2x= 3x - 9-2x\)

Then, you will have \(\displaystyle x\) by itself on the right side of the equation:

\(\displaystyle 4= x - 9\)

Next, you add \(\displaystyle 9\) to both sides of the equation to put all of the numbers on the same side of the equation:

\(\displaystyle 4+9= x - 9+9\)

\(\displaystyle 13= x\)

Once you do this, you have found that \(\displaystyle x=13\).

1.) Add 5 to both sides, removing the "\(\displaystyle -5\)". It now reads \(\displaystyle 10x+10=20x\).

2.) Subtract \(\displaystyle 10x\) from both sides, removing the "\(\displaystyle 10x\)". It now reads \(\displaystyle 10=10x\).

3.) Divide both sides by 10, resulting in \(\displaystyle x=1\)

1.) Distribute the 6, which ends up as \(\displaystyle 6x+30=17x-25\).

2.) Add 25 to both sides, removing the "\(\displaystyle -25\)". It now reads \(\displaystyle 6x+55=17x\)

3.) Subtract \(\displaystyle 6x\) from both sides, removing the "\(\displaystyle 6x\)". It now reads \(\displaystyle 55=11x\)

4.) Divide both sides by 11, resulting in \(\displaystyle 5=x\)

\(\displaystyle 15z + 70 = 280\) 

Subtract \(\displaystyle 70\) from both sides

\(\displaystyle 15z= 210\) 

Divide both sides by \(\displaystyle 15\)

\(\displaystyle z = 14\)