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Solve for all values of
x in simplest form.

8+5|x-10|=23
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $8+5|x-10|=23$ $\newline$ Answer: $x=$

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Solve logarithmic equations with multiple logarithms

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

8+5|x-10|=23

\newline

Answer:

x=

Isolate absolute value expression: Isolate the absolute value expression by subtracting $8$ from both sides of the equation. $\newline$ $8 + 5|x - 10| = 23$ $\newline$ $5|x - 10| = 23 - 8$ $\newline$ $5|x - 10| = 15$
Divide by $5$ : Divide both sides of the equation by $5$ to solve for the absolute value expression. $\newline$ $\frac{5|x - 10|}{5} = \frac{15}{5}$ $\newline$ $|x - 10| = 3$
Split into two equations: Split the equation into two separate equations to account for the absolute value. $x - 10 = 3$ or $x - 10 = -3$
Solve for x ( $1$ st equation): Solve the first equation for x. $\newline$ $x - 10 = 3$ $\newline$ $x = 3 + 10$ $\newline$ $x = 13$
Solve for x ( $2$ nd equation): Solve the second equation for x. $\newline$ $x - 10 = -3$ $\newline$ $x = -3 + 10$ $\newline$ $x = 7$

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