Mathematics 10 — Exercise Review · Q11

Full question

The actual GPS location is 100 m and the error is at most 6 m: |100−r|≤6. Find acceptable reported locations r.

Step-by-step solution

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

   $$(-6,100-x,6)$$

2. Subtract the inside constant from all three parts.

   $$(-6-100,-x,6-100)$$

3. Calculate both endpoint subtractions.

   $$(-106,-x,-94)$$

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

   $$(-\frac{106}{-1},x,-\frac{94}{-1})$$

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

   $$[94,106]$$

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

   $$[94,106]$$

Answer

The final answer is shown below.