Certainly! Let's simplify the expression step-by-step.
Given expression:
[tex]\[ 2x - [x - 3 - (4x - 5)] \][/tex]
Step 1: Simplify the innermost parentheses [tex]\((4x - 5)\)[/tex]:
[tex]\[ 4x - 5 \][/tex]
Step 2: Substitute back into the expression inside the brackets [tex]\((x - 3 - (4x - 5))\)[/tex]:
[tex]\[ x - 3 - (4x - 5) \][/tex]\
This can be written as:
[tex]\[ x - 3 - 4x + 5 \][/tex]
Step 3: Combine like terms inside the brackets:
[tex]\[ (x - 4x) + (-3 + 5) \][/tex]
[tex]\[ -3x + 2 \][/tex]
Step 4: Substitute “-3x + 2” back into the original expression:
[tex]\[ 2x - [-3x + 2] \][/tex]
Step 5: Simplify the expression:
[tex]\[ 2x - (-3x + 2) \][/tex]
[tex]\[ 2x + 3x - 2 \][/tex]
Step 6: Combine like terms:
[tex]\[ (2x + 3x) - 2 \][/tex]
[tex]\[ 5x - 2 \][/tex]
After the simplification, we obtain:
[tex]\[ 5x - 2 \][/tex]
This matches option [tex]\((D)\)[/tex].
Therefore, the simplified expression is:
[tex]\[ \boxed{5x - 2} \][/tex]
Matching the choice [tex]\( D) 5x - 2 \)[/tex].
