To determine which step should NOT be completed when evaluating the linear expression for [tex]\( x = 5 \)[/tex]:
[tex]\[ x + 5 + \frac{3x}{5} - 4 \][/tex]
Let's examine each option carefully:
A. Adding 5 and -4
Adding the constants 5 and -4 is a legitimate simplification:
[tex]\[ 5 - 4 = 1 \][/tex]
This can and should be done to simplify the expression.
B. Adding [tex]\( x \)[/tex] and [tex]\( 3x \)[/tex]
Adding like terms is valid here. Since [tex]\( x \)[/tex] and [tex]\( 3x \)[/tex] are like terms:
[tex]\[ x + 3x = 4x \][/tex]
This can and should be done to simplify the expression.
C. Simplifying the term [tex]\( \frac{3x}{5} \)[/tex] to 3
Let's check the correctness of simplifying [tex]\( \frac{3x}{5} \)[/tex] specifically for [tex]\( x = 5 \)[/tex]:
[tex]\[ \frac{3x}{5} = \frac{3 \cdot 5}{5} = \frac{15}{5} = 3 \][/tex]
This works when [tex]\( x = 5 \)[/tex], but this simplification is not generally correct for just any [tex]\( x \)[/tex]. The term [tex]\( \frac{3x}{5} \)[/tex] should remain [tex]\( \frac{3x}{5} \)[/tex] unless specifically evaluated for [tex]\( x = 5 \)[/tex]. Hence, simplifying [tex]\( \frac{3x}{5} \)[/tex] to 3 is incorrect as a general rule for the expression.
D. Rewriting the expression as [tex]\( x + \frac{3x}{5} + 5 - 4 \)[/tex]
Rewriting the expression by changing the order of terms while preserving the operations does not alter its value:
[tex]\[ x + 5 + \frac{3x}{5} - 4 \][/tex]
is equivalent to:
[tex]\[ x + \frac{3x}{5} + 5 - 4 \][/tex]
This step is legitimate and can be completed.
Given these evaluations, the step that should NOT be completed is:
[tex]\[ \boxed{C} \][/tex]
Simplifying the term [tex]\( \frac{3x}{5} \)[/tex] to 3 is not correct as a general simplification for any [tex]\( x \)[/tex], only for the specific case where [tex]\( x = 5 \)[/tex].
