Final answer:
To solve the inequality -2 [8x - 4] < 2x + 5, distribute -2 in the brackets, combine like terms, and isolate x to find that the solution is x > 1/6.
Step-by-step explanation:
To solve the linear inequality -2 [8x - 4] < 2x + 5, we first distribute the -2 into the parentheses:
-2 × 8x gives us -16x, and -2 × -4 gives us +8, resulting in the inequality -16x + 8 < 2x + 5.
Next, we move all x terms to one side by adding 16x to both sides of the inequality:
+16x -16x + 8 < 2x + 16x + 5, simplifying to 8 < 18x + 5.
Then, we isolate the x term by subtracting 5 from both sides:
8 - 5 < 18x + 5 - 5, which simplifies to 3 < 18x.
Finally, we divide both sides by 18 to solve for x:
3/18 < x, or x > 1/6.
So, the solution to the inequality is x > 1/6.