Question

2. (x+1) (x+2) - (x-3) (x + 4) 6​

Answer 1

Ответ:

x∈[-4;∞)

Объяснение:

(x+1)(x+2)-(x-3)(x+4)≥6

(x+1)(x+2)-(x-3)(x+4)≥6

x²+3x+2-(x²+x-12)≥6

x²+3x+2-x²-x+12≥6

2x+14≥6

2x≥-8

x≥-4

x∈[-4;∞)

Answer 2

To simplify the given expression $(x+1)(x+2) - (x-3)(x+4)$, you can start by using the distributive property to expand both sets of parentheses and then combine like terms. Here's how you can do it step by step:

1. Expand the first set of parentheses: $(x+1)(x+2) = x(x+2) + 1(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2$

2. Expand the second set of parentheses: $(x-3)(x+4) = x(x+4) - 3(x+4) = x^2 + 4x - 3x - 12 = x^2 + x - 12$

3. Substitute the expanded expressions back into the original expression: $(x^2 + 3x + 2) - (x^2 + x - 12)$

4. Distribute the negative sign through the second set of parentheses: $(x^2 + 3x + 2) - x^2 - x + 12$

5. Combine like terms: $x^2 + 3x + 2 - x^2 - x + 12 = 3x + 2 - x + 12 = 2x + 14$

So, the simplified expression is $2x + 14$.