Type an absolute value equation for 'the numbers a distance of 18 from 3.'
Understand the Problem
The question is asking for the formulation of an absolute value equation that represents numbers that have a distance of 18 from 3. This involves setting up an equation based on the definition of absolute value, which captures the distance from a point on a number line.
Answer
The absolute value equation is $$ |x - 3| = 18 $$
Answer for screen readers
The absolute value equation is
$$ |x - 3| = 18 $$
Steps to Solve
- Understand the absolute value definition
The absolute value of a number represents its distance from zero on the number line. Therefore, the equation for the distance from a number can be expressed using absolute value.
- Set up the equation with the given distance
We are given that the distance must be 18 from the number 3. We can represent this mathematically as:
$$ |x - 3| = 18 $$
- Interpret the equation
The equation $|x - 3| = 18$ indicates that the distance between ( x ) and 3 is equal to 18. This basically means ( x ) can be either 18 units to the left or right of 3.
The absolute value equation is
$$ |x - 3| = 18 $$
More Information
This equation indicates that there are two possible solutions for ( x ): one when it is 18 units greater than 3 and one when it is 18 units less than 3. Thus, the solutions are ( x = 21 ) and ( x = -15 ), which you can find by solving the absolute value equation.
Tips
- Forgetting the absolute value: When stating distances, always remember to use the absolute value symbol.
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