To determine which of the following expressions are equivalent to [tex]\( -5.93 + (-8.62) + 5.93 \)[/tex], let's simplify and compare each option step-by-step.
First, simplify the original expression:
[tex]\[ -5.93 + (-8.62) + 5.93 \][/tex]
Notice that [tex]\( -5.93 \)[/tex] and [tex]\( +5.93 \)[/tex] are additive inverses, meaning they sum up to zero:
[tex]\[ (-5.93 + 5.93) = 0 \][/tex]
So, the original expression simplifies to:
[tex]\[ 0 + (-8.62) = -8.62 \][/tex]
Thus, the original expression [tex]\( -5.93 + (-8.62) + 5.93 \)[/tex] simplifies to [tex]\( -8.62 \)[/tex].
Next, let's evaluate each option:
1. Option (A):
[tex]\[ -8.62 \][/tex]
This is exactly the same as the simplified original expression, so this option is equivalent.
2. Option (B):
[tex]\[ -5.93 + (-5.93) - 8.62 \][/tex]
Simplify this step-by-step:
[tex]\[ -5.93 + (-5.93) = -11.86 \][/tex]
So, the expression becomes:
[tex]\[ -11.86 - 8.62 \][/tex]
Clearly, [tex]\(-11.86 - 8.62\)[/tex] is not equivalent to [tex]\(-8.62\)[/tex]. Thus, this option is not equivalent.
3. Option (C):
[tex]\[ 8.62 - 5.93 + 5.93 \][/tex]
Simplify the additions and subtractions:
[tex]\[ -5.93 + 5.93 = 0 \][/tex]
Therefore, the expression simplifies to:
[tex]\[ 8.62 + 0 = 8.62 \][/tex]
Clearly, [tex]\(8.62\)[/tex] is not equivalent to [tex]\(-8.62\)[/tex]. Thus, this option is not equivalent.
4. Option (D):
[tex]\[ (5.93 - 5.93) - 8.62 \][/tex]
Simplify the parentheses first:
[tex]\[ 5.93 - 5.93 = 0 \][/tex]
So, the expression becomes:
[tex]\[ 0 - 8.62 = -8.62 \][/tex]
This is exactly the same as the simplified original expression, so this option is equivalent.
Therefore, the two expressions that are equivalent to [tex]\( -5.93 + (-8.62) + 5.93 \)[/tex] are:
- (A) [tex]\(-8.62\)[/tex]
- (D) [tex]\((5.93 - 5.93) - 8.62\)[/tex]
