Mathematics 10 — Exercise Review · Q7 (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.

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

2. Subtract the inside constant from all three parts.

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

3. Calculate both endpoint subtractions.

   $$(-8,-2\times x,-6)$$

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

   $$(-\frac{8}{-2},x,-\frac{6}{-2})$$

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

   $$[3,4]$$

6. 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.