Mathematics 10 — Exercise 4.2 · Q2 (iii)

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.

   $$(4\times x-9=3,4\times x-9=-3)$$

2. Subtract the inside constant from both sides.

   $$4\times x=3+9$$

3. Calculate this subtraction.

   $$4\times x=12$$

4. Divide both sides by the coefficient of x.

   $$x=\frac{12}{4}$$

5. Reduce the fraction to obtain this solution.

   $$x=3$$

6. Subtract the inside constant from both sides.

   $$4\times x=-3+9$$

7. Calculate this subtraction.

   $$4\times x=6$$

8. Divide both sides by the coefficient of x.

   $$x=\frac{6}{4}$$

9. Reduce the fraction to obtain this solution.

   $$x=\frac{3}{2}$$

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

    $$\{\frac{3}{2},3\}$$

Answer

The final answer is shown below.