Question

Machine 1 can complete a task in x hours while an upgraded machine (machine 2) needs 9 fewer hours. The plant manager knows the two machines will take at least 6 hours, as represented by the inequality:
1/x+1/x-9 more than or equal to 1/6
Which answer choice includes all solutions to the inequality and identifies which interval(s) contain viable completion times of
machine 1?

Answer 1

Answer:

B

Step-by-step explanation:

E D G E N U I T Y

Answer 2

Solutions to the inequality to identify the interval is given by

(0,3] ∪(9,18], (9,18] contains viable times of machine 1.

What is inequality?

" Inequality is defined as the relation between the variables as per the given situation using sign of inequality >, <, ≤, ≥."

According to the question,

Time taken by machine 1 can complete a task = x hours

Time taken by machine 2 can complete a task = (x-9)hours

Time taken by two machines to complete a task  at least 6 hours

Given inequality to represent the relation

$\frac{1}{x} + \frac{1}{x-9} \geq \frac{1}{6}$

Simplify the inequality we get,

$\frac{x-9+x}{(x)(x-9)} \geq \frac{1}{6}\\\\\implies \frac{2x-9}{(x)(x-9)} \geq \frac{1}{6}\\\\\implies 6(2x-9) \geq x^{2} -9x\\\\\implies 12x-54 \geq x^{2} -9x\\\\\implies x^{2} -9x-12x+54\leq 0\\\\\implies x^{2} -21x+54\leq 0\\\\\implies x^{2} -18x-3x+54\leq 0\\\\\implies (x-18)(x-3) \leq 0$

Therefore,

x ≤ 18 or x≤ 3

Hence, solutions to the inequality to identify the interval is given by

(0,3] ∪(9,18], (9,18] contains viable times of machine 1.

Learn more about inequality here

https://brainly.com/question/20383699

#SPJ2