Mathematics

Problem

In a school laboratory the air temperature

T

(in

^{\circ}

C) must stay at least

-2^{\circ}

C but be lower than

6^{\circ}

C. a. (i) Write a linear inequality that represents the acceptable values of

T

. b. (ii) The heater is controlled by a knob reading

y

so that

T=0.5y-4

. Form a linear inequality in

y

that guarantees the temperature requirement in part (i). c. (iii) Solve the inequality obtained in part (ii). d. (iv) Represent the admissible values of

y

on a number line with appropriate end-points and shading.

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