Mathematics 10 — Exercise 4.2 · Q2 (iv)

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.

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

2. Subtract the inside constant from both sides.

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

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.

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

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.

    $$\{3,4\}$$

Answer

The final answer is shown below.