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The least amount is 98 and the greatest amount is 122 that the two friends could spend on food given that food budget is modeled by 1/2|x-110| = 6. This can be obtained by using the definition of absolute value function.
What are the least and greatest amounts that the two friends could spend on food?
The absolute value function is defined by:
- f(x) = x, x ≥ 0.
- f(x) = x, x < 0.
Therefore the one example of the absolute value function is:
⇒ |x| = a means that x = a or x = -a.
Here in the question it is given that,
- The equation is 1/2|x - 110| = 6
By simplifying the equation we get,
1/2|x - 110| = 6
Multiplying both sides by 2 we get,
⇒ |x - 110| = 6 × 2
⇒ |x - 110| = 12
By applying the definition of the absolute value function, we can write that,
x - 110 = -12 or x - 110 = 12.
- For the least amount, we have,
x - 110 = -12
⇒ x = 98
- For the greatest amount, we have,
x - 110 = 12
⇒ x = 122
Hence the least amount is 98 and the greatest amount is 122 that the two friends could spend on food given that food budget is modeled by 1/2|x-110| = 6.
Learn more about absolute value function here:
brainly.com/question/10664936
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