Let's break down the expression:
[tex]\[ 7 + (-12) + (-3) \][/tex]
1. First, let's handle the addition of 7 and -12:
[tex]\[ 7 + (-12) \][/tex]
Adding a positive number and a negative number can be thought of as subtracting the smaller absolute value from the larger absolute value and keeping the sign of the larger absolute value.
Here, the absolute values are 7 and 12. Since 12 is larger:
[tex]\[ 7 + (-12) = -5 \][/tex]
2. Now, we'll take the result from the first step and add -3:
[tex]\[ -5 + (-3) \][/tex]
3. Adding two negative numbers involves adding their absolute values and then making the result negative:
The absolute values are 5 and 3. Adding them:
[tex]\[ 5 + 3 = 8 \][/tex]
And since both numbers were negative, the result is:
[tex]\[ -8 \][/tex]
So, the final result of the expression [tex]\( 7 + (-12) + (-3) \)[/tex] is:
[tex]\[ -8 \][/tex]
