Mathematics 10 — Exercise 4.2 · Q2 (i)

Full question

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

Step-by-step solution

1. An absolute value equals C when its inside expression equals C or −C.

   $$(x-2=6,x-2=-6)$$

2. Subtract the inside constant from both sides.

   $$x=6+2$$

3. Calculate this subtraction.

   $$x=8$$

4. Divide both sides by the coefficient of x.

   $$x=8\times \frac{1}{1}$$

5. Reduce the fraction to obtain this solution.

   $$x=8$$

6. Subtract the inside constant from both sides.

   $$x=-6+2$$

7. Calculate this subtraction.

   $$x=-4$$

8. Divide both sides by the coefficient of x.

   $$x=-4\times \frac{1}{1}$$

9. Reduce the fraction to obtain this solution.

   $$x=-4$$

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

    $$\{-4,8\}$$

Answer

The final answer is shown below.