Mathematics 10 — Exercise 4.2 · Q3 (i)

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.

   $$(-3,5\times x+8,3)$$

2. Subtract the inside constant from all three parts.

   $$(-3-8,5\times x,3-8)$$

3. Calculate both endpoint subtractions.

   $$(-11,5\times x,-5)$$

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

   $$(-\frac{11}{5},x,-\frac{5}{5})$$

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

   $$[-\frac{11}{5},-1]$$

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

   $$[-\frac{11}{5},-1]$$

Answer

The final answer is shown below.