if $f(x) = 16x - 30$ and $g(x) = 14x - 6$, for which value of $x$ does $(f - g)(x) = 0$?

-18
-12
12
18

Question

if $f(x) = 16x - 30$ and $g(x) = 14x - 6$, for which value of $x$ does $(f - g)(x) = 0$?

-18
-12
12
18

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Subtraction" ], "new_concepts": [], "current_concepts": [ "Function Subtraction", "Polynomial Operations" ] } ## Define the difference function $$ (f - g)(x) = f(x) - g(x) = (16x - 30) - (14x - 6) $$ ## Simplify the expression $$ (f - g)(x) = 16x - 30 - 14x + 6 = 2x - 24 $$ ## Solve for x when the difference is zero $$ \begin{aligned} 2x - 24 &= 0 \ 2x &= 24 \ x &= 12 \end{aligned} $$

(A) $-18$

(B) $-12$

(C) $12$

(D) $18$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Subtraction" ] }

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QUESTION IMAGE

Question

Explanation:

Define the difference function

Simplify the expression

Solve for x when the difference is zero

Answer: