139k views
4 votes
Solve the inequality. Give solution set in interval notation.

-4(x+2) > 3x+ 20

User Olvlvl
by
8.2k points

1 Answer

3 votes

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, ∞).

User Mythago
by
8.6k points

No related questions found