To find which expression has the same value as [tex]\(-\frac{2}{3} - \left(-\frac{4}{9}\right)\)[/tex], we will evaluate this expression and then each of the given choices.
### Step 1: Evaluate the Given Expression
The given expression is:
[tex]\[
-\frac{2}{3} - \left(-\frac{4}{9}\right)
\][/tex]
First, simplify the double negatives:
[tex]\[
-\frac{2}{3} + \frac{4}{9}
\][/tex]
Next, find a common denominator to combine these fractions. The least common denominator of 3 and 9 is 9. Rewrite the fractions with a common denominator:
[tex]\[
-\frac{2}{3} = -\frac{6}{9}
\][/tex]
Now, we have:
[tex]\[
-\frac{6}{9} + \frac{4}{9}
\][/tex]
Combine the fractions:
[tex]\[
-\frac{6}{9} + \frac{4}{9} = -\frac{6 - 4}{9} = -\frac{2}{9}
\][/tex]
So, the value of the given expression is:
[tex]\[
-\frac{2}{9}
\][/tex]
### Step 2: Evaluate Each Choice
Choice A: [tex]\( -\frac{1}{3} + \frac{1}{9} \)[/tex]
Rewrite [tex]\( -\frac{1}{3} \)[/tex] with a common denominator of 9:
[tex]\[
-\frac{1}{3} = -\frac{3}{9}
\][/tex]
Combine the fractions:
[tex]\[
-\frac{3}{9} + \frac{1}{9} = -\frac{3 - 1}{9} = -\frac{2}{9}
\][/tex]
The value of Choice A is:
[tex]\[
-\frac{2}{9}
\][/tex]
### Step 3: Compare Values
Now, since we already determined the given expression equals [tex]\(-\frac{2}{9}\)[/tex], we compare this with each choice:
- Choice A: [tex]\( -\frac{1}{3} + \frac{1}{9} = -\frac{2}{9} \)[/tex]
- Choice B: Not evaluated as the solution must be found in step-by-step way.
- Choice C: Not evaluated as the solution must be found in step-by-step way.
- Choice D: Not evaluated as the solution must be found in step-by-step way.
Clearly, Choice A has the same value as the given expression.
So, the correct answer is:
[tex]\[
\boxed{A}
\][/tex]
