Mathematics 10 — Exercise 4.2 · Q2 (ii)

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.

   $$(2\times x+1=7,2\times x+1=-7)$$

2. Subtract the inside constant from both sides.

   $$2\times x=7-1$$

3. Calculate this subtraction.

   $$2\times x=6$$

4. Divide both sides by the coefficient of x.

   $$x=\frac{6}{2}$$

5. Reduce the fraction to obtain this solution.

   $$x=3$$

6. Subtract the inside constant from both sides.

   $$2\times x=-7-1$$

7. Calculate this subtraction.

   $$2\times x=-8$$

8. Divide both sides by the coefficient of x.

   $$x=-\frac{8}{2}$$

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.

    $$\{-4,3\}$$

Answer

The final answer is shown below.