Show that no real solution, x, exists for the inequality |3x - 7| + 5 <= 0

| 3x - 7 | + 5 <= 0

| 3x - 7 | <= -5 ................... subtracted 5 from both sides

But | 3x - 7 | can never <= -5 ...............

Why not? Because we know | 3x - 7 | =>0 for all x..............

How do we know that? By the law of absolute value.

Hope that helps :)

|3x - 7| + 5 <= 0?
|3x - 7| <= -5

Since the absolute value of a number is always positive there is no solution for this inequality. An absolute value cannot equal or be < -5.

for every x |3x - 7|=>0 +5 is always >0