Part 1013 Completed: 18 of 20 My score: \( 18 / 20 \mathrm{pts}(90 \% \) Solve the linear inequality. Express the solution set using set-builder and interval notation: Graph the solution set. \[ 8(x+5)-4 x>7(x-1)+35 \] The solution set expressed in set-builder notation is \( \{x \mid \)

We start with the inequality:   8(x + 5) – 4x > 7(x – 1) + 35 Step 1. Distribute on both sides:   LHS: 8(x + 5) – 4x = 8x + 40 – 4x = 4x + 40   RHS: 7(x – 1) + 35 = 7x – 7 + 35 = 7x + 28 So the inequality becomes:   4x + 40 > 7x + 28 Step 2. Isolate the variable x:   Subtract 4x from both sides:    40 > 3x + 28   Subtract 28 from both sides:    12 > 3x   Divide both sides by 3:    4 > x This can be rewritten as:   x < 4 Step 3. Express the solution in the requested forms: Set-builder notation:   {x ∈ ℝ | x < 4} Interval notation:   (–∞, 4) Graphing the solution: On a number line, draw an open circle at 4 (since 4 is not included) and shade the line extending to the left toward negative infinity. Thus, the final answer is:   Set-builder: {x ∈ ℝ | x < 4}   Interval: (–∞, 4)