Solve the inequality. Graph the solution set, and write the solution set in set-builder notation and inter integers. \( -5 t-5<-(t+2)-4 t \)

We start with the inequality   –5t – 5 < –(t + 2) – 4t. Step 1. Simplify the right side:   –(t + 2) – 4t = –t – 2 – 4t = –5t – 2. Now the inequality becomes:   –5t – 5 < –5t – 2. Step 2. Add 5t to both sides to eliminate the t-term:   (–5t – 5) + 5t < (–5t – 2) + 5t   –5 < –2. Step 3. Analyze the result:   The inequality –5 < –2 is always true. This means that no matter what value t takes, the original inequality holds. Solution in Different Forms: 1. Interval Notation:   The solution set is (–∞, ∞). 2. Set-Builder Notation:   { t ∈ ℝ }. 3. Integer Solution:   Since every real number is a solution, every integer is also a solution. In other words, the solution set among the integers is ℤ (all integers). Graphing the Solution Set:   Draw a horizontal number line.   Shade the entire line, indicating that every point on the line is included.   Place open circles (or no special point marks) everywhere to show there are no restrictions. Thus, the inequality is true for all t, so the solution set is all real numbers (and hence all integers).