Two friends are planning for a gathering. the food budget is modeled by one half times the absolute value of the quantity x minus 120 end quantity equals 10 comma where x is the amount spent on food. what are the least and greatest amounts that the two friends could spend on food?

absolutevalue of |x| {modulus of x} is the value of areal numberx. The least andgreatestamounts that the twofriendscould spend onfoodare 100 and 140, respectively.## What is Absolute Value?

absolutevalue of |x| {modulus of x} is the value of areal numberx, the value we get is always anon-negativenumber, for example, |-5| willgive5, and also, |5| will give 5 as well.budgetis modeled as (1/2)|x – 120|=10, where x is the amount spent on food.equationfor the absolute quantity the critical point is 120. Therefore, we can write,valueof x≥120,valueof x isgreaterthan 120, the absolutequantitywill be positive,valueof x<120,valueof x is less than 120, theabsolute quantitywill be negative,greatestamounts that the twofriendscould spend onfoodare 100 and 140, respectively.Absolute valuehere: