Question

3x+4/x+1<2 решите рациональное неравенство

Answer 1

Вот сама решила не списывала

Answer 2

To solve the rational inequality $\frac{3x+4}{x+1} < 2$, we need to find the values of $x$ that satisfy the inequality. Here's how to do it step by step:

Step 1: Get a common denominator. Multiply both sides of the inequality by $x+1$ to eliminate the denominator: $(x+1) \cdot \frac{3x+4}{x+1} < 2 \cdot (x+1)$

Step 2: Simplify. Cancel out the common factor of $x+1$ on the left side: $3x + 4 < 2x + 2$

Step 3: Move variables to one side. Subtract $2x$ from both sides to get all $x$ terms on the left side: $3x - 2x + 4 < 2$

Step 4: Simplify further. Combine the $x$ terms on the left side: $x + 4 < 2$

Step 5: Isolate $x$ on one side. Subtract 4 from both sides to isolate $x$ on the left side: $x < 2 - 4$

Step 6: Final result. Simplify the right side: $x < -2$

So the solution to the rational inequality is $x < -2$.