To determine which expression is equivalent to [tex]\( -1.3 + (-4.9) + (-2.6) \)[/tex], let's evaluate each option step-by-step to see which one matches the original expression.
First, let's calculate the value of the original expression:
[tex]\[ -1.3 + (-4.9) + (-2.6) \][/tex]
[tex]\[ = -1.3 - 4.9 - 2.6 \][/tex]
[tex]\[ = -8.8 \][/tex]
Now, let's evaluate the given options to see if any of them equal [tex]\(-8.8\)[/tex].
1. [tex]\((1.3 + 4.9 + 2.6)\)[/tex]
Let's add them:
[tex]\[ 1.3 + 4.9 + 2.6 \][/tex]
[tex]\[ = 1.3 + 4.9 = 6.2 \][/tex]
[tex]\[ 6.2 + 2.6 = 8.8 \][/tex]
So, this expression equals [tex]\( 8.8 \)[/tex], not [tex]\(-8.8\)[/tex]. Therefore, this is not equivalent to the original expression.
2. [tex]\(-(1.3 - 4.9) + (-2.6)\)[/tex]
Let's first evaluate inside the parentheses:
[tex]\[ 1.3 - 4.9 \][/tex]
Since [tex]\( 4.9 \)[/tex] is larger than [tex]\( 1.3 \)[/tex]:
[tex]\[ = -3.6 \][/tex]
Now, apply the negative sign outside:
[tex]\[ -( -3.6 ) = 3.6 \][/tex]
Add [tex]\( -2.6 \)[/tex]:
[tex]\[ 3.6 + (-2.6) \][/tex]
[tex]\[ = 3.6 - 2.6 \][/tex]
[tex]\[ = 1.0 \][/tex]
So, this expression equals [tex]\( 1 \)[/tex], not [tex]\( -8.8 \)[/tex]. Therefore, this is not equivalent to the original expression.
3. [tex]\(-1.3 + (4.9 + 2.6)\)[/tex]
Let's add the numbers inside the parentheses first:
[tex]\[ 4.9 + 2.6 \][/tex]
[tex]\[ = 7.5 \][/tex]
Now, add [tex]\( -1.3 \)[/tex]:
[tex]\[ -1.3 + 7.5 \][/tex]
[tex]\[ = 6.2 \][/tex]
So, this expression equals [tex]\( 6.2 \)[/tex], not [tex]\( -8.8 \)[/tex]. Therefore, this is not equivalent to the original expression.
4. [tex]\(-1.3 - (4.9 + 2.6)\)[/tex]
Let's add the numbers inside the parentheses first:
[tex]\[ 4.9 + 2.6 \][/tex]
[tex]\[ = 7.5 \][/tex]
Now, subtract from [tex]\( -1.3 \)[/tex]:
[tex]\[ -1.3 - 7.5 \][/tex]
[tex]\[ = -8.8 \][/tex]
So, this expression equals [tex]\( -8.8 \)[/tex], which matches the original expression.
Therefore, the expression that is equivalent to [tex]\( -1.3 + (-4.9) + (-2.6) \)[/tex] is:
[tex]\[ -1.3 - (4.9 + 2.6) \][/tex]
