Question

Log1/2 (2x + 1) > - 2

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the inequality $\log_{\frac{1}{2}}(2x + 1) > -2$, we need to find the range of values for $x$ that satisfy the inequality. Here's the step-by-step solution:

Step 1: Rewrite the inequality using exponential form. Since $\log_{\frac{1}{2}}(2x + 1) > -2$, we can rewrite it as: $\left(\frac{1}{2}\right)^{-2} < 2x + 1$

Step 2: Simplify the left side of the inequality. $\left(\frac{1}{2}\right)^{-2} = 2^2 = 4$

Step 3: Now the inequality becomes: $4 < 2x + 1$

Step 4: Subtract 1 from both sides: $3 < 2x$

Step 5: Divide both sides by 2: $\frac{3}{2} < x$

So, the solution for the inequality is $x > \frac{3}{2}$ or in interval notation: $x \in \left(\frac{3}{2}, \infty\right)$.