Mathematics 10 — Exercise 4.3 · Q6

Full question

A chemical process must stop when |T−37|>2.5 °C. Find the stop temperatures.

Step-by-step solution

1. For an outside bound the inside expression is less than −C OR greater than C. Include equality only for ≥.

   $$(x-37,-\frac{5}{2},\frac{5}{2})$$

2. For this branch subtract the constant from both sides.

   $$(x,-\frac{5}{2}+37)$$

3. Divide by the coefficient; reverse this branch’s sign if the coefficient is negative.

   $$(x,\frac{69}{2})$$

4. For this branch subtract the constant from both sides.

   $$(x,\frac{5}{2}+37)$$

5. Divide by the coefficient; reverse this branch’s sign if the coefficient is negative.

   $$(x,\frac{79}{2})$$

6. Combine the valid branch(es) into the following interval or union. Empty intervals contribute no solutions.

   $$(-\infty ,\frac{69}{2})\cup (\frac{79}{2},\infty )$$

7. Draw each endpoint open for < or >, filled for ≤, ≥ or an equation solution. Shade the allowed intervals.

   $$(-\infty ,\frac{69}{2})\cup (\frac{79}{2},\infty )$$

Answer

The final answer is shown below.