We can split this absolute value inequality into two inequalities:
1a) (x-3) ≥ 2x+1 x - 3 ≥ 2x + 1 -x ≥ 4 x ≤ -4
1b) -(x-3) ≥ 2x+1
x + 3 ≥ 2x + 1 2x ≤ 2 x ≤ 1
Combining the solutions from (1a) and (1b), we have x ≤ -4 or x ≤ 1.
2) |2x+3|
Since there is no inequality sign provided, we cannot solve for a specific range of x. The absolute value of 2x+3 can be expressed as follows: |2x+3| = 2x+3 if 2x+3 ≥ 0, or |2x+3| = -(2x+3) if 2x+3 < 0.
1) |x-3| ≥ 2x+1
We can split this absolute value inequality into two inequalities:
1a) (x-3) ≥ 2x+1
x - 3 ≥ 2x + 1
-x ≥ 4
x ≤ -4
1b) -(x-3) ≥ 2x+1
x + 3 ≥ 2x + 12x ≤ 2
x ≤ 1
Combining the solutions from (1a) and (1b), we have x ≤ -4 or x ≤ 1.
2) |2x+3|
Since there is no inequality sign provided, we cannot solve for a specific range of x. The absolute value of 2x+3 can be expressed as follows: |2x+3| = 2x+3 if 2x+3 ≥ 0, or |2x+3| = -(2x+3) if 2x+3 < 0.