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Which values of
x are solutions of the equation
(5)/(x)=(x+13)/(6) ? Select all that apply.
A.
◻
-15
B.
◻ 15
C.
◻ 2
D.
◻
-3
E.
◻
-10
F.
◻
-2

Which values of $x$ are solutions of the equation $\frac{5}{x}=\frac{x+13}{6}$ ? Select all that apply. $\newline$ A. $\square$ $-15$ $\newline$ B. $\square$ $15$ $\newline$ C. $\square$ $2$ $\newline$ D. $\square$ $-3$ $\newline$ E. $\square$ $-10$ $\newline$ F. $\square$ $\frac{5}{x}=\frac{x+13}{6}$ $1$

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Solve complex trigonomentric equations

Full solution

Q. Which values of

x

are solutions of the equation

\frac{5}{x}=\frac{x+13}{6}

? Select all that apply.

\newline

A.

\square

-15

\newline

B.

\square

15

\newline

C.

\square

2

\newline

D.

\square

-3

\newline

E.

\square

-10

\newline

F.

\square

\frac{5}{x}=\frac{x+13}{6}

1

Simplify the equation: Now, simplify the equation. $30 = x^2 + 13x$
Move terms and set to zero: Next, move all terms to one side to set the equation to zero. $x^2 + 13x - 30 = 0$
Factor the quadratic equation: Now, factor the quadratic equation. $\newline$ $(x + 15)(x - 2) = 0$
Set factors equal and solve: Set each factor equal to zero and solve for $x$ . $x + 15 = 0$ or $x - 2 = 0$
Solve first equation: Solve the first equation. $x = -15$
Solve second equation: Solve the second equation. $x = 2$
Check solutions: Check the solutions in the original equation to make sure they don't cause division by zero or any other issues. $\newline$ For $x = -15$ : $\newline$ $\frac{5}{-15} = \frac{-15 + 13}{6}$ $\newline$ $-\frac{1}{3} = -\frac{2}{6}$ $\newline$ $-\frac{1}{3} = -\frac{1}{3}$ , which is true.
Check solutions: Check the solutions in the original equation to make sure they don't cause division by zero or any other issues. $\newline$ For $x = -15$ : $\newline$ $\frac{5}{-15} = \frac{-15 + 13}{6}$ $\newline$ $-\frac{1}{3} = -\frac{2}{6}$ $\newline$ $-\frac{1}{3} = -\frac{1}{3}$ , which is true.For $x = 2$ : $\newline$ $\frac{5}{2} = \frac{2 + 13}{6}$ $\newline$ $\frac{5}{2} = \frac{15}{6}$ $\newline$ $\frac{5}{2} = 2.5$ , but $\frac{15}{6} = 2.5$ , which is true.

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