Solve for all values of x in simplest form. -|4x-8|-7=-16 Answer: x=

Isolate Absolute Value Expression: Isolate the absolute value expression by adding 7 to both sides of the equation. -|4x - 8| - 7 = -16 -|4x - 8| - 7 + 7 = -16 + 7 -|4x - 8| = -9Divide to Remove Negative Sign: Divide both sides by -1 to get rid of the negative sign in front of the absolute value. -1 * -|4x - 8| = -1 * -9 |4x - 8| = 9Set Up Two Equations: Set up two equations to solve for x, because the absolute value of a number can be either positive or negative. 4x - 8 = 9 or 4x - 8 = -9Solve for x (Equation 1): Solve the first equation for x. 4x - 8 = 9 4x = 9 + 8 4x = 17 x = 17 / 4 x = 4.25Solve for x (Equation 2): Solve the second equation for x. 4x - 8 = -9 4x = -9 + 8 4x = -1 x = -1 / 4 x = -0.25

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Solve for all values of
x in simplest form.

-|4x-8|-7=-16
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $-|4 x-8|-7=-16$ $\newline$ Answer: $x=$

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Algebra 2

Solve absolute value equations

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

-|4 x-8|-7=-16

\newline

Answer:

x=

Isolate Absolute Value Expression: Isolate the absolute value expression by adding $7$ to both sides of the equation. $\newline$ $-|4x - 8| - 7 = -16$ $\newline$ $-|4x - 8| - 7 + 7 = -16 + 7$ $\newline$ $-|4x - 8| = -9$
Divide to Remove Negative Sign: Divide both sides by $-1$ to get rid of the negative sign in front of the absolute value. $\newline$ $-1 \times -|4x - 8| = -1 \times -9$ $\newline$ $|4x - 8| = 9$
Set Up Two Equations: Set up two equations to solve for $x$ , because the absolute value of a number can be either positive or negative. $\newline$ $4x - 8 = 9$ or $4x - 8 = -9$
Solve for x (Equation $1$ ): Solve the first equation for x. $\newline$ $4x - 8 = 9$ $\newline$ $4x = 9 + 8$ $\newline$ $4x = 17$ $\newline$ $x = \frac{17}{4}$ $\newline$ $x = 4.25$
Solve for x (Equation $2$ ): Solve the second equation for x. $\newline$ $4x - 8 = -9$ $\newline$ $4x = -9 + 8$ $\newline$ $4x = -1$ $\newline$ $x = -\frac{1}{4}$ $\newline$ $x = -0.25$