using the solution to a literal equation

when the equation $a - bx = cx + d$ is solved for $x$, the result is $x = \frac{a - d}{b + c}$.

use the general solution to solve $5 - 6x = 8x + 17$.

Question

using the solution to a literal equation

when the equation $a - bx = cx + d$ is solved for $x$, the result is $x = \frac{a - d}{b + c}$.

use the general solution to solve $5 - 6x = 8x + 17$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Literal Equations" ], "new_concepts": [], "current_concepts": [ "Literal Equations", "Algebraic Rearrangement" ] } ## Identify parameters by matching equations $$ \begin{aligned} &a - bx = cx + d \ &5 - 6x = 8x + 17 \ &a = 5,\quad b = 6,\quad c = 8,\quad d = 17 \end{aligned} $$ ## Substitute values into general solution $$ \begin{aligned} &x = \frac{a - d}{b + c} \ &x = \frac{5 - 17}{6 + 8} \end{aligned} $$ ## Simplify the expression $$ \begin{aligned} &x = \frac{-12}{14} \ &x = -\frac{6}{7} \end{aligned} $$ When the equation $a - bx = cx + d$ is solved for $x$, the result is $x = \frac{a-d}{b+c}$. Use the general solution to solve $5 - 6x = 8x + 17$. $-\frac{6}{7}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Literal Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify parameters by matching equations

Substitute values into general solution

Simplify the expression

Answer: