Mathematics 10 — Exercise 4.2 · Q3 (vi)

Full question

Solve the following absolute-value equation or inequality and represent its solution set on a number line.

Step-by-step solution

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

   $$(1-2\times x,-5,5)$$

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

   $$(-2\times x,-5-1)$$

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

   $$(x,-\frac{6}{-2})$$

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

   $$(-2\times x,5-1)$$

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

   $$(x,\frac{4}{-2})$$

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

   $$(-\infty ,-2)\cup (3,\infty )$$

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

   $$(-\infty ,-2)\cup (3,\infty )$$

Answer

The final answer is shown below.