Step-by-step explanation
1. Rewrite the equation without absolute value bars
Use the rules:
→ and →
to write all four options of the equation
without the absolute value bars:
When simplified, equations and are the same and equations and are the same, so we end up with only 2 equations:
| , | |
| , |
2. Solve the two equations for z
Add to both sides:
Simplify the arithmetic:
Simplify the arithmetic:
Divide both sides by the coefficient:
NT_MSLUS_MAINSTEP_RESOLVE_DOUBLE_MINUS:
Subtract from both sides:
Simplify the arithmetic:
Simplify the arithmetic:
Divide both sides by the coefficient:
3. List the solutions
(2 solution(s))
4. Graph
Each line represents the function of one side of the equation:
The equation is true where the two lines cross.
How did we do?
Please leave us feedback.Why learn this
We encounter absolute values almost daily. For example: If you walk 3 miles to school, do you also walk minus 3 miles when you go back home? The answer is no because distances use absolute value. The absolute value of the distance between home and school is 3 miles, there or back.
In short, absolute values help us deal with concepts like distance, ranges of possible values, and deviation from a set value.