Sure, let's use the Associative Property of Addition to simplify the given expression step-by-step:
Given expression:
[tex]\[ 24 + 18 + (-9) + (-12) \][/tex]
Step 1: Grouping the numbers in pairs to simplify. We can rearrange the addition to make it easier to handle:
[tex]\[ (24 + 18) + ((-9) + (-12)) \][/tex]
Step 2: Add the numbers within each group:
[tex]\[ 24 + 18 = 42 \][/tex]
and
[tex]\[ (-9) + (-12) = -21 \][/tex]
Step 3: Now, add the results from each of the groups together:
[tex]\[ 42 + (-21) \][/tex]
Step 4: Finally, perform the addition:
[tex]\[ 42 + (-21) = 21 \][/tex]
So, the simplified result of the expression [tex]\( 24 + 18 + (-9) + (-12) \)[/tex] is [tex]\( 21 \)[/tex].
