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Solve for all values of
x in simplest form.

9-5|3-4x|=-31
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $9-5|3-4 x|=-31$ $\newline$ Answer: $x=$

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Solve absolute value equations

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

9-5|3-4 x|=-31

\newline

Answer:

x=

Isolate absolute value expression: Isolate the absolute value expression. $\newline$ Add $31$ to both sides of the equation to isolate the absolute value term. $\newline$ $9 - 5|3 - 4x| + 31 = -31 + 31$ $\newline$ $40 - 5|3 - 4x| = 0$ $\newline$ Now, divide both sides by $-5$ to get the absolute value by itself. $\newline$ $(40 - 5|3 - 4x|) / -5 = 0 / -5$ $\newline$ $-8 + |3 - 4x| = 0$
Divide by $-5$ : Isolate the absolute value. $\newline$ Add $8$ to both sides of the equation to get the absolute value by itself. $\newline$ -8 + 8 + |3 - 4x| = 0 + 8\(\newline|3 - 4x| = 8\)
Isolate absolute value: Set up two equations to remove the absolute value. $\newline$ Since $|A| = B$ implies $A = B$ or $A = -B$ , we have two cases: $\newline$ Case $1$ : $3 - 4x = 8$ $\newline$ Case $2$ : $3 - 4x = -8$
Set up equations: Solve for $x$ in Case $1$ . $\newline$ $3 - 4x = 8$ $\newline$ Subtract $3$ from both sides. $\newline$ $-4x = 8 - 3$ $\newline$ $-4x = 5$ $\newline$ Now, divide by $-4$ to solve for $x$ . $\newline$ $x = 5 / -4$ $\newline$ $x = -5/4$
Solve for x in Case $1$ : Solve for x in Case $2$ . $\newline$ $3 - 4x = -8$ $\newline$ Subtract $3$ from both sides. $\newline$ $-4x = -8 - 3$ $\newline$ $-4x = -11$ $\newline$ Now, divide by $-4$ to solve for x. $\newline$ $x = -11 / -4$ $\newline$ $x = 11/4$

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\newline

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\newline

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