Let's solve each of the given expressions step-by-step, providing detailed explanations for each.
1. Evaluate [tex]\( -45 + (-48) \)[/tex]:
When we add two negative numbers, we add their absolute values and keep the negative sign.
- Absolute value of [tex]\(-45\)[/tex] is [tex]\(45\)[/tex].
- Absolute value of [tex]\(-48\)[/tex] is [tex]\(48\)[/tex].
Add these absolute values together:
[tex]\[ 45 + 48 = 93 \][/tex]
Since we are adding two negative numbers, the result is negative:
[tex]\[ -45 + (-48) = -93 \][/tex]
2. Evaluate [tex]\( 30 + (-26) \)[/tex]:
When we add a positive number to a negative number, we subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.
- Absolute value of [tex]\(30\)[/tex] is [tex]\(30\)[/tex].
- Absolute value of [tex]\(-26\)[/tex] is [tex]\(26\)[/tex].
Subtract the smaller absolute value from the larger absolute value:
[tex]\[ 30 - 26 = 4 \][/tex]
Since the positive number has the larger absolute value, the result is positive:
[tex]\[ 30 + (-26) = 4 \][/tex]
Thus, we have the solutions:
1. [tex]\( -45 + (-48) = -93 \)[/tex]
2. [tex]\( 30 + (-26) = 4 \)[/tex]
So the final results are:
[tex]\[ (-93, 4) \][/tex]
