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Solve for all values of
x in simplest form.

4+|5x+4|=7
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $4+|5 x+4|=7$ $\newline$ Answer: $x=$

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Evaluate absolute value expressions

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

4+|5 x+4|=7

\newline

Answer:

x=

Write Given Equation: Write down the given equation. $\newline$ We have the equation $4 + |5x + 4| = 7$ . $\newline$ We need to find the value of $x$ that satisfies this equation.
Isolate Absolute Value: Isolate the absolute value expression. $\newline$ Subtract $4$ from both sides of the equation to isolate the absolute value on one side. $\newline$ $4 + |5x + 4| - 4 = 7 - 4$ $\newline$ $|5x + 4| = 3$
Set Up Two 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: $\newline$ Case $1$ : $5x + 4 = 3$ $\newline$ Case $2$ : $5x + 4 = -3$
Solve Case $1$ : Solve for $x$ in Case $1$ . $\newline$ Subtract $4$ from both sides of the first case equation. $\newline$ $5x + 4 - 4 = 3 - 4$ $\newline$ $5x = -1$ $\newline$ Now, divide both sides by $5$ to solve for $x$ . $\newline$ $x = -\frac{1}{5}$
Solve Case $2$ : Solve for $x$ in Case $2$ . $\newline$ Subtract $4$ from both sides of the second case equation. $\newline$ $5x + 4 - 4 = -3 - 4$ $\newline$ $5x = -7$ $\newline$ Now, divide both sides by $5$ to solve for $x$ . $\newline$ $x = -7 / 5$

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