Solving absolute value equations
Solving absolute value equations
An absolute value or modulus of a real number is always positive. Therefore, when solving absolute value equations, we need to establish two cases for each equation. One case is to set the quantity inside the absolute value notation as positive; whereas another case is to set the value as negative.
Basic concepts:
 Solving polynomial equations
 Solving quadratic equations by factoring
 Solving quadratic equations by completing the square
 Absolute value functions
Related concepts:
 Solving radical equations
 Solving rational equations
Lessons

1.
Solving Equations with One Absolute Value
Solve each absolute value equation:
i) algebraically
ii) verify the solution graphically
a)
$\left {x + 4} \right = 5x  2$


2.
Solving Equations with Two Absolute Values
Solve each absolute value equation:
i) algebraically
ii) verify the solution graphically