Which of the following statements is always false when x=3 y=2 and z=4

The correct answer is: [A]: " 1(x) = 1 " .
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→ { that is: " 1 *(x) = 1 " . } .
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Explanation:
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Note:
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The question asks:
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Which of the following statements is always false when:

→ " x = 3 " , " y = 2 " ,  and: " z = 4 " ?
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with the following answer choices:
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[A]: " 1* (x) = 1 " ;

[B]: " 0 * (x) = 0 " .

[C]: " x + y = y + x " ;

[D]: " x(y + z) = xy + xz " .
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→ Let us consider each answer choice; and plug in the known values:
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Choice: [A]: " 1* (x) = 1 " ;
Note: We are given: " x = 3 " ; so; plug in "3" and solve:

→ 1(3) = " 3 "; and " 3 ≠ 1 " .

Furthermore: Given: " 1(x) = 1 " ; in the answer choice ;

Note that, on the "left-hand side" of the equation:

→ 1(x) = 1 * x = x * 1 = "x" ;

→ since "any value" ; multiplied by "1" ; equals that same value.

→ As such, substitute: "x" (in lieu of "1x") ; on the "left-hand side" of the equation ; and:

→ REWRITE the equation:

→ " x = 1 " ;

→  Since we are given: "x = 3" ; substitute "3" for "x" in the equation, as follows:

→ " 3 = 1 " ; which is INCORRECT;

    → since: " 3 ≠ 1 " .

→ This answer is ALWAYS false; so:

Answer choice: [A]: " 1(x) = 1 " ; should be CORRECT.
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Choice: [B]: " 0 * (x) = 0 " ;

Note: We are given: " x = 3 " ; so; plug in "3" and solve:

→ 0(3) = 0 ; which is: "true" in this case.

→ As such, this answer is NOT "always false" ;

→ and: Answer choice: [B]: is INCORRECT.
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Choice: [C]: " x + y = y + x " ;

Note: We are given: " x = 3 " ; AND: " y = 2 " ;

So plug in these given values into the equation:

  → 3 + 2 = 2 + 3 ;

  → 5 = 5. Yes!

→ As such, this answer is NOT "always false" ;

→ and: Answer choice: [C]: is INCORRECT.
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Choice: [D]: " x(y + z) = xy + xz " ;

Note: We are given: " x = 3 " ;  " y = 2 " ; AND:  " z = 4 " ;

So plug in these given values into the equation:

  → 3(2 + 4) = (3*2) + (3*4)  ;

→. 3(6) = 6 + 12 ;

  → 18 = 18. Yes!

→ As such, this answer is NOT "always false" ;

→ and: Answer choice: [D]: is INCORRECT.
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So; the correct answer is:
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Answer choice: [A]: " 1(x) = 1 " .
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→ { that is: " 1 *(x) = 1 " . } .
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Hope this answer—and lengthy explanation—helps!
Best wishes in the Brainly community—and in your academic pursuits!