Questions: Solve. -x-1>0 x>-1 No solution -1<x<1 ∞<x<∞

Transcript text: Solve. \[ -|x|-1>0 \] $x>-1$ No solution $-1

Solution

Solution Steps

Step 1: Analyze the inequality

The given inequality is: \[ -|x| - 1 > 0 \] This can be rewritten as: \[ -|x| > 1 \]

Step 2: Solve for $|x|$

Multiply both sides of the inequality by $-1$. Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign: \[ |x| < -1 \]

Step 3: Interpret the result

The absolute value of any real number $x$, $|x|$, is always non-negative. Therefore, $|x| < -1$ is impossible because $|x|$ cannot be less than a negative number. This means there is no real number $x$ that satisfies the inequality.

Step 4: Conclusion

The inequality has no solution. The correct answer is: \[ \text{No solution} \]