Algebra Tutorials!
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

Solving Absolute Value Equations

Solving an Equation of the Form | z| = |w|

The equation |z| = |w| says that the distance on a number line from z to 0 the same as the distance from w to 0. So, z and w must be equal or they must be opposites.

This can be summarized in the following principle:

Principle

Absolute Value Equations of the Form | z| = |w|

In the equation |z| = |w|,

let z and w represent any algebraic expressions.

Then, either z and w are equal: z = w or z and w are opposites: z = -w.

Note:

If z and w are equal, then they are at the same location on a number line.

If z and w are opposites, then they are the same distance from zero on a number line, but on opposite sides of 0.

 We will use this principle to solve this equation: Replace x + 6 with z and 2x with w. Rewrite the absolute value equation as two equations.Replace z with x + 6 and w with 2x. Subtract x from both sides. In the equation on the right, divide both sides by -3. |x + 6| = |2x||z| = |w| z = w or z = -wx + 6 = 2x or x + 6 = -2x6 = x or 6 = -3x6 = x or -2 = x
Thus, the solutions to |x + 6| = |2x| are x = 6 and x = -2.