Question

(x+1)*(x-3)-(x-4)*(x+4)>3 (2x-5)/3>=-3 это система

Answer 1

Решение смотри на фото

Answer 2

To solve this system of inequalities, let's work on each inequality separately and then find the intersection of their solutions:

Inequality 1: $(x+1) \cdot (x-3) - (x-4) \cdot (x+4) > 3$

Expand both terms: $x^2 - 2x - 3 - (x^2 - 16) > 3$

Simplify: $-2x + 13 > 3$

Subtract 13 from both sides: $-2x > -10$

Divide by -2 (remember to reverse the inequality because we're dividing by a negative number): $x < 5$

Inequality 2: $\frac{2x-5}{3} \geq -3$

Multiply both sides by 3 to eliminate the fraction: $2x - 5 \geq -9$

Add 5 to both sides: $2x \geq -4$

Divide by 2: $x \geq -2$

Now we have two separate inequalities:

1. $x < 5$
2. $x \geq -2$

To find the intersection of these solution sets, we need to find the range where both inequalities are satisfied:

The overlapping range is from $x \geq -2$ to $x < 5$.

So, the solution to the system of inequalities is: $-2 \leq x < 5$