Question

Two friends are planning for a gathering. the food budget is modeled by one half times the absolute value of the quantity x minus 130 end quantity equals 8 comma where x is the amount spent on food. what are the least and greatest amounts that the two friends could spend on food? $126, $134 $122, $138 $114, $146 $57, $73

Answer 1

Using the absolute value function, the least and greatest amounts that the two friends could spend on food are $114 and $146. so C choice is correct.

The absolute value function is defined by:

f(x) = x, x ≥ 0.

f(x) = x, x < 0.

Hence, the example of the function is:

|x| = a means that x = a or x = -a.

In this given problem, the equation is:

$\frac{1}{2}$|x - 130| = 8

0.5|x - 130| = 8

Then, removing the 0.5:

|x - 130| = 8/0.5

|x - 130| = 16

Applying the definition of the absolute value function, we have that

x - 130 = -16 or x - 130 = 16

For the least amount, we have that;

x - 130 = -16 -> x = $114

For the greatest amount, we have that;

x - 130 = 16 -> x = $146

More can be learned about the absolute value function at;

brainly.com/question/24514895

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