Final answer:
To solve the inequality 2.5x - 4 ≥ 2(1.5x + 4), distribute, combine like terms, isolate the variable, and solve for x and we get x ≤ -24. .
Step-by-step explanation:
To solve the inequality 2.5x - 4 ≥ 2(1.5x + 4), we can start by distributing the 2 on the right side of the equation:
2.5x - 4 ≥ 3x + 8
Next, we can combine like terms by subtracting 3x from both sides:
2.5x - 3x - 4 ≥ 8
-0.5x - 4 ≥ 8
Then, we can isolate the variable by adding 4 to both sides:
-0.5x ≥ 12
Finally, we can divide both sides by -0.5, remembering to flip the inequality sign since we are dividing by a negative number:
x ≤ -24
So the values that make this inequality true are x ≤ -24.