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 $5 - 6x = 8x + 17$.

Explanation:

Step1: Identify values of a, b, c, d

In the equation \(5 - 6x = 8x + 17\), compare with \(a - bx = cx + d\). So \(a = 5\), \(b = 6\), \(c = 8\), \(d = 17\).

Step2: Substitute into the formula \(x=\frac{a - d}{b + c}\)

Substitute the values: \(x=\frac{5 - 17}{6 + 8}\).

Step3: Simplify numerator and denominator

Numerator: \(5 - 17=-12\). Denominator: \(6 + 8 = 14\). So \(x=\frac{-12}{14}\).

Step4: Reduce the fraction

Simplify \(\frac{-12}{14}\) by dividing numerator and denominator by 2: \(x =-\frac{6}{7}\).

Answer:

\(x =-\frac{6}{7}\)