Mathematics 10 — Exercise Review · Q6 (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.

   $$(6\times x+1=9,6\times x+1=-9)$$

2. Subtract the inside constant from both sides.

   $$6\times x=9-1$$

3. Calculate this subtraction.

   $$6\times x=8$$

4. Divide both sides by the coefficient of x.

   $$x=\frac{8}{6}$$

5. Reduce the fraction to obtain this solution.

   $$x=\frac{4}{3}$$

6. Subtract the inside constant from both sides.

   $$6\times x=-9-1$$

7. Calculate this subtraction.

   $$6\times x=-10$$

8. Divide both sides by the coefficient of x.

   $$x=-\frac{10}{6}$$

9. Reduce the fraction to obtain this solution.

   $$x=-\frac{5}{3}$$

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

    $$\{-\frac{5}{3},\frac{4}{3}\}$$

Answer

The final answer is shown below.