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the number of devices must be less than 18

the maximum number of devices is 17 for which the cost of the new plan is less that the cost of the current plan

step-by-step explanation:

we know that

the inequality that represent this situation is equal to

solve for x

subtract 94 both sides

divide by 4.50 both sides

therefore

the number of devices must be less than 18

so

the maximum number of devices is 17 for which the cost of the new plan is less that the cost of the current plan

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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