Question

Fill in the blank with $<$, $>$or $=$:

$(-21)-(-10)\_\_\_\_\_(-31)+(-11)$

Answer 1

Step 1: Evaluate the expression on the left-hand side (L.H.S)

L.H.S $=(-21)-(-10)$

To subtract an integer $b$ from another integer $a$, we add the additive inverse of $b$ to $a$. So, $a-b=a+(-b)$.

$\Rightarrow$L.H.S $=(-21)+10$ ( as the additive inverse of $-10$ is $10$)

$\Rightarrow$L.H.S $=-11$

Step 2: Evaluate the expression on the right-hand side (R.H.S)

R.H.S $=(-31)+(-11)$

The sum of two negative integers is calculated by adding the integers' absolute values and putting a minus sign in the result.

$\Rightarrow$R.H.S $=-42$

Step 3: Compare L.H.S and R.H.S

L.H.S $=-11$

R.H.S $=-42$

L.H.S $>$R.H.S.

Hence, $(-21)-(-10)>(-31)+(-11)$.