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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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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. $\newline$ $4x - 8 = -9$ $\newline$ $4x = -9 + 8$ $\newline$ $4x = -1$ $\newline$ $x = -\frac{1}{4}$ $\newline$ $x = -0.25$

More problems from Solve absolute value equations

Question

3 n^{2}=27

\newline

What are the solutions to the given equation?

\newline

1

\newline

n=\sqrt{3}

\newline

n=3

\newline

n=-\sqrt{3}

n=\sqrt{3}

\newline

n=-3

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\newline

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\newline

1

\newline

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\newline

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Question

\$200

with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get

40

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\newline

1

\newline

40h+80t=400

\newline

80h+40t=200

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5h+2.5t=200

\newline

2.5h+5t=200

Posted 2 months ago