3. Solving Absolute Value Equations
Sign In
The first step is isolating the absolute value expression.
See solution.
There are two main steps when solving an absolute value equation.
| Step 1 | Isolate the absolute value expression. |
|---|---|
| Step 2 | If the absolute value expression is equal to a positive number, solve both arising equations from the disjunction (positive and negative). There are two solutions. |
| If the absolute value expression is equal to zero, remove the absolute value and solve the equation. There is one solution. | |
| If the absolute value expression is equal to a negative number, there is no solution. |
Let's see examples for these cases.
lc 2x-1 ≥ 0:2x-1 = 5 & (I) 2x-1 < 0:2x-1 = - 5 & (II)
(I), (II): LHS+1=RHS+1
(I), (II): .LHS /2.=.RHS /2.