Mathematics 10 — Exercise Review · Q7 (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. The inside expression must lie between −C and C. Use strict or inclusive bounds exactly as given.

   $$(-24,6\times x+18,24)$$

2. Subtract the inside constant from all three parts.

   $$(-24-18,6\times x,24-18)$$

3. Calculate both endpoint subtractions.

   $$(-42,6\times x,6)$$

4. Divide all parts by the coefficient. If it is negative, reverse BOTH inequality signs.

   $$(-\frac{42}{6},x,\frac{6}{6})$$

5. Combine the valid branch(es) into the following interval or union. Empty intervals contribute no solutions.

   $$[-7,1]$$

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

   $$[-7,1]$$

Answer

The final answer is shown below.