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Solve for all values of
x in simplest form.

2+3|5+5x|=35
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $2+3|5+5 x|=35$ $\newline$ Answer: $x=$

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Evaluate absolute value expressions

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

2+3|5+5 x|=35

\newline

Answer:

x=

Divide by $3$ : Now, divide both sides of the equation by $3$ to solve for the absolute value expression: $\newline$ $|5 + 5x| = \frac{33}{3}$ $\newline$ $|5 + 5x| = 11$
Split into Two Equations: The absolute value equation $|5 + 5x| = 11$ can split into two separate equations because if the expression inside the absolute value is positive, it equals $11$ , and if it's negative, it equals $-11$ . $\newline$ So we have two cases: $\newline$ $5 + 5x = 11$ (when the expression inside is positive) $\newline$ $5 + 5x = -11$ (when the expression inside is negative)
Solve Positive Case: Let's solve the first case: $\newline$ $5 + 5x = 11$ $\newline$ Subtract $5$ from both sides to isolate the term with $x$ : $\newline$ $5x = 11 - 5$ $\newline$ $5x = 6$ $\newline$ Now, divide both sides by $5$ to solve for $x$ : $\newline$ $x = \frac{6}{5}$ $\newline$ $x = 1.2$
Solve Negative Case: Now let's solve the second case: $\newline$ $5 + 5x = -11$ $\newline$ Subtract $5$ from both sides to isolate the term with $x$ : $\newline$ $5x = -11 - 5$ $\newline$ $5x = -16$ $\newline$ Now, divide both sides by $5$ to solve for $x$ : $\newline$ $x = -16 / 5$ $\newline$ $x = -3.2$

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