Final answer:
To solve the inequality -4(x + 4) > x + 7, distribute -4, combine like terms, and isolate the variable x. The solution is x < -23/5, which can be represented as the interval (-∞, -23/5).
Step-by-step explanation:
To solve the inequality -4(x + 4) > x + 7, we need to simplify and isolate the variable x on one side of the inequality. Here's the step-by-step process:
- Distribute -4 to both terms inside the parentheses: -4x - 16 > x + 7
- Add 4x to both sides to get rid of the variable on the left side: -16 > 5x + 7
- Subtract 7 from both sides to isolate the variable: -23 > 5x
- Finally, divide both sides by 5 to solve for x: x < -23/5
The solution to the inequality is x < -23/5, which means that x is any number less than -23/5. This can be represented as the interval (-∞, -23/5).