Write the inequality in interval notation. Then graph the interval.
x ≤ - 6 or x > 0
Interval notation: (-∞, -6] U (0, ∞)
Graph: 
Solve and graph the equation.
│x│= 7
To solve the equation │x│= 7, we need to consider two cases:
Case 1: x is positive.
In this case, │x│ is equal to x. So the equation becomes x = 7. Solving for x, we have x = 7.
Case 2: x is negative.
In this case, │x│ is equal to -x. So the equation becomes -x = 7. Solving for x, we have x = -7.
Therefore, the solutions to the equation │x│= 7 are x = 7 and x = -7.
Graph:
The graph of │x│= 7 consists of two horizontal lines, one at y = 7 and the other at y = -7, intersecting the x-axis at x = -7 and x = 7.
│3t│= 24
To solve the equation │3t│= 24, we need to consider two cases:
Case 1: 3t is positive.
In this case, │3t│ is equal to 3t. So the equation becomes 3t = 24. Solving for t, we have t = 8.
Case 2: 3t is negative.
In this case, │3t│ is equal to -3t. So the equation becomes -3t = 24. Solving for t, we have t = -8.
Therefore, the solutions to the equation │3t│= 24 are t = 8 and t = -8.
Graph:
The graph of │3t│= 24 consists of two vertical lines, one at x = 8 and the other at x = -8, intersecting the y-axis at y = 24 and y = -24.
│x + 9│≥ 4
To solve the inequality │x + 9│≥ 4, we need to consider two cases:
Case 1: x + 9 is positive or zero.
In this case, │x + 9│ is equal to x + 9. So the inequality becomes x + 9 ≥ 4. Solving for x, we have x ≥ -5.
Case 2: x + 9 is negative.
In this case, │x + 9│ is equal to -(x + 9). So the inequality becomes -(x + 9) ≥ 4. Solving for x, we have x ≤ -13.
Therefore, the solutions to the inequality │x + 9│≥ 4 are x ≥ -5 or x ≤ -13.
Graph:
The graph of │x + 9│≥ 4 consists of two half-lines, one going to the right from x = -5, and the other going to the left from x = -13.
│x│+ 7 = 13
To solve the equation │x│+ 7 = 13, we need to consider two cases:
Case 1: x is positive.
In this case, │x│ is equal to x. So the equation becomes x + 7 = 13. Solving for x, we have x = 6.
Case 2: x is negative.
In this case, │x│ is equal to -x. So the equation becomes -x + 7 = 13. Solving for x, we have x = -6.
Therefore, the solutions to the equation │x│+ 7 = 13 are x = 6 and x = -6.
Graph:
The graph of │x│+ 7 = 13 consists of two vertical lines, one at x = 6 and the other at x = -6, intersecting the y-axis at y = 13.