Solve: |3x + 7| ¡Ý 26
To solve the inequality |3x + 7| ≥ 26, we need to consider two cases:
Case 1: (3x + 7) ≥ 26
In this case, we can solve for x:
3x + 7 ≥ 26
3x ≥ 26 - 7
3x ≥ 19
x ≥ 19/3
Case 2: -(3x + 7) ≥ 26
In this case, we need to solve for x and remember to flip the inequality sign when multiplying or dividing by a negative number:
-(3x + 7) ≥ 26
-3x - 7 ≥ 26
-3x ≥ 26 + 7
-3x ≥ 33
x ≤ 33/(-3)
x ≤ -11
Therefore, the solution to the inequality |3x + 7| ≥ 26 is:
x ≤ -11 or x ≥ 19/3.
You can graph this situation on a number line by marking the values -11 and 19/3 and shading the sections to the left of -11 and to the right of 19/3 to include the respective values.