Question

which sign makes the statement true? |-53| ? |-33| > < =

Explanation:

Step1: Calculate absolute values

The absolute value of a number \( x \) is \( |x|=

$$\begin{cases}x, & x\geq0\\ -x, & x < 0\end{cases}$$

\). For \( |- 53| \), since \( - 53<0 \), \( |-53|=-(-53) = 53 \). For \( |-33| \), since \( -33 < 0 \), \( |-33|=-(-33)=33 \).

Step2: Compare the two values

We compare \( 53 \) and \( 33 \). Since \( 53>33 \), we have \( |-53|>|-33| \).

Answer:

\( > \)