Solve for all values of x in simplest form. 10+|2x+5|=22 Answer: x=

Isolate absolute value: Write down the equation and isolate the absolute value expression. We have the equation 10 + |2x + 5| = 22. To isolate the absolute value, we subtract 10 from both sides of the equation. 10 + |2x + 5| - 10 = 22 - 10 |2x + 5| = 12Set up equations: Set up two separate equations to account for the absolute value. Since the absolute value of a number can be either positive or negative, we have two cases: 2x + 5 = 12 or 2x + 5 = -12Solve positive case: Solve the first equation where the inside of the absolute value is positive. 2x + 5 = 12 Subtract 5 from both sides: 2x = 12 - 5 2x = 7 Divide both sides by 2: x = 7 / 2 x = 3.5Solve negative case: Solve the second equation where the inside of the absolute value is negative. 2x + 5 = -12 Subtract 5 from both sides: 2x = -12 - 5 2x = -17 Divide both sides by 2: x = -17 / 2 x = -8.5

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Solve for all values of
x in simplest form.

10+|2x+5|=22
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $10+|2 x+5|=22$ $\newline$ Answer: $x=$

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Precalculus

Solve logarithmic equations with multiple logarithms

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Q. Solve for all values of

x

in simplest form.

\newline

10+|2 x+5|=22

\newline

Answer:

x=

Isolate absolute value: Write down the equation and isolate the absolute value expression. $\newline$ We have the equation $10 + |2x + 5| = 22$ . To isolate the absolute value, we subtract $10$ from both sides of the equation. $\newline$ $10 + |2x + 5| - 10 = 22 - 10$ $\newline$ $|2x + 5| = 12$
Set up equations: Set up two separate equations to account for the absolute value. $\newline$ Since the absolute value of a number can be either positive or negative, we have two cases: $\newline$ $2x + 5 = 12$ or $2x + 5 = -12$
Solve positive case: Solve the first equation where the inside of the absolute value is positive. $\newline$ $2x + 5 = 12$ $\newline$ Subtract $5$ from both sides: $\newline$ $2x = 12 - 5$ $\newline$ $2x = 7$ $\newline$ Divide both sides by $2$ : $\newline$ $x = \frac{7}{2}$ $\newline$ $x = 3.5$
Solve negative case: Solve the second equation where the inside of the absolute value is negative. $\newline$ $2x + 5 = -12$ $\newline$ Subtract $5$ from both sides: $\newline$ $2x = -12 - 5$ $\newline$ $2x = -17$ $\newline$ Divide both sides by $2$ : $\newline$ $x = \frac{-17}{2}$ $\newline$ $x = -8.5$