Mathematics 10 — Exercise 4.3 · Q7

Full question

Rods must be 2.5 m long with tolerance ±0.04 m. Find acceptable lengths from |x−2.5|≤0.04.

Step-by-step solution

1. The inside expression must lie between −C and C. Use strict or inclusive bounds exactly as given.

   $$(-\frac{1}{25},x-\frac{5}{2},\frac{1}{25})$$

2. Subtract the inside constant from all three parts.

   $$(-\frac{1}{25}+\frac{5}{2},x,\frac{1}{25}+\frac{5}{2})$$

3. Calculate both endpoint subtractions.

   $$(\frac{123}{50},x,\frac{127}{50})$$

4. Divide all parts by the coefficient. If it is negative, reverse BOTH inequality signs.

   $$(\frac{123}{50},x,\frac{127}{50})$$

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

   $$[\frac{123}{50},\frac{127}{50}]$$

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

   $$[\frac{123}{50},\frac{127}{50}]$$

Answer

The final answer is shown below.