Write and solve an inequality for the situation. Tom is deciding whether he should become a member of a gym to use the basketball courts. The membership costs $135. Then, members will pay $3 each time they rent out the courts. Nonmembers can also rent the courts for $11 each time. How many times would Tom have to rent the basketball courts in order for his cost as a member to be cheaper than the cost of a nonmember? As a member, Tom's cost would be cheaper if he rents the courts or more times.

As a member, Tom's cost would be cheaper if he rents the courts 17 or more times.

Step-by-step explanation:

Let the number of times be x

If Tom is a member, and rents the courts x number of times, then he would pay

$135 + $3 × x = $135 + $3x

For a nonmember that rents x number of times, the nonmember would pay

$11 × x = $11x

Now, we are to determine which value of x for which $135 + $3x is less than $11x, that is

$135 + $3x < $11x

Solving the inequality,

$135 < $11x - $3x

$135 < $8x

$135 / $8 < x

16.875 < x

∴ x > 16.875

This means, for Tom's cost to be cheaper, he must have rented the court for more than 16.875 times. (Round 16.875 to the nearest whole number)

16.875 ≅ 17

∴ x > 17

Hence, As a member, Tom's cost would be cheaper if he rents the courts 17 or more times.

you are saying it as if a fact, not a question, but yes, you would be correct? ; )

step-by-step explanation:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.