Final answer:
To solve the inequality -4(x+2) > 3x + 20, distribute the -4, combine like terms, and divide by -7, remembering to reverse the inequality sign. The solution in interval notation is (-∞, -4).
Step-by-step explanation:
To solve the inequality -4(x+2) > 3x + 20, we follow these steps:Distribute the -4 across the parentheses: -4x - 8 > 3x + 20.Move all terms involving x to one side: -4x - 3x > 20 + 8.Combine like terms: -7x > 28Divide both sides by -7, remembering to reverse the inequality sign because we're dividing by a negative number: x < -4.The solution set in interval notation is (-∞, -4).
To solve the inequality -4(x+2) > 3x+20, we can start by distributing the -4 on the left side of the equation, which gives us -4x - 8 > 3x + 20. Next, we can combine like terms by adding 4x to both sides, which gives us -8 > 7x + 20. Then, we can subtract 20 from both sides, which gives us -28 > 7x. Finally, we can divide both sides by 7 to solve for x, which gives us -4 < x.The solution set in interval notation is (-4, ∞).