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Solve for $v$ . $\newline$ $10 = |\text{-}v|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $v =$ _ or $v =$ _

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Solve absolute value equations

Full solution

Q. Solve for

v

.

\newline

10 = |\text{-}v|

\newline

Write your answers as integers or as proper or improper fractions in simplest form.

\newline

v =

_____ or

v =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation is $10 = |\text{-}v|$ . The absolute value of a number is always non-negative, so $|\text{-}v|$ can be either $10$ or $-10$ . However, since the absolute value is always non-negative, we only consider the positive value, which is $10$ .
Set up two equations: Set up two equations based on the definition of absolute value. $\newline$ Since $|-v|$ can be either $10$ or $-10$ , we set up two equations to solve for $v$ : $\newline$ $1$ ) $-v = 10$ $\newline$ $2$ ) $-v = -10$
Solve first equation: Solve the first equation for $v$ . Starting with the first equation $\text{–}v = 10$ , we multiply both sides by $-1$ to solve for $v$ : $v = -10$
Solve second equation: Solve the second equation for $v$ . Now, we solve the second equation $\text{–}v = \text{–}10$ by multiplying both sides by $-1$ : $v = 10$
Check solutions: Check the solutions. $\newline$ We substitute $v = -10$ and $v = 10$ back into the original equation to verify the solutions: $\newline$ For $v = -10$ : $10 = |–(-10)| = |10| = 10$ (True) $\newline$ For $v = 10$ : $10 = |–(10)| = |-10| = 10$ (True) $\newline$ Both solutions satisfy the original equation.

More problems from Solve absolute value equations

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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

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\newline

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\newline

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Question

\$200

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\newline

1

\newline

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\newline

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\newline

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\newline

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