\( 1 \leftarrow \quad \begin{array}{r}\text { Solve and graph the solution set. } \\ 21 x(x-7)<3(7 x-1)(x-8)\end{array} \)

We want to solve the inequality   21·x(x – 7) < 3·(7x – 1)(x – 8). Step 1. Expand both sides. • Expand the left side:   21·x(x – 7) = 21x² – 147x. • Expand the right side:   (7x – 1)(x – 8) = 7x² – 57x + 8,   then multiply by 3:   3(7x² – 57x + 8) = 21x² – 171x + 24. So the inequality becomes:   21x² – 147x < 21x² – 171x + 24. Step 2. Simplify the inequality. Subtract 21x² from both sides:   –147x < –171x + 24. Add 171x to both sides:   24x < 24. Divide both sides by 24 (since 24 > 0, the inequality sign does not change):   x < 1. Step 3. Write the solution. The inequality holds for all x such that x < 1. Step 4. Graph the solution on a number line. • Draw a horizontal line. • Mark the point x = 1 with an open circle (since 1 is not included in the solution). • Shade or draw an arrow pointing to the left of 1, which indicates all numbers less than 1. Thus, the solution set is   {x ∈ ℝ : x < 1} or in interval notation, (–∞, 1).