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Solve for $q$ . $\newline$ $|-3q| = 3$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $q =$ _ or $q =$ _

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Solve absolute value equations

Full solution

Q. Solve for

q

.

\newline

|-3q| = 3

\newline

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

\newline

q =

_____ or

q =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $|-3q| = 3$ means that the absolute value of $-3q$ is equal to $3$ . The absolute value of a number is its distance from zero on the number line, which means it is always non-negative. Therefore, $-3q$ can either be $3$ or $-3$ .
Set up two equations: Set up two separate equations to solve for $q$ . Since the absolute value of $–3q$ is $3$ , we can write two equations: one for the positive case and one for the negative case. Equation $1$ : $–3q = 3$ Equation $2$ : $–3q = -3$
Solve first equation for q: Solve the first equation for q. $\newline$ Starting with Equation $1$ : $-3q = 3$ $\newline$ Divide both sides by $-3$ to isolate $q$ . $\newline$ $q = \frac{3}{-3}$ $\newline$ $q = -1$
Solve second equation for $q$ : Solve the second equation for $q$ . Now, solve Equation $2$ : $-3q = -3$ Divide both sides by $-3$ to isolate $q$ . $q = -3 / -3$ $q = 1$

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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Question

\$200

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\newline

1

\newline

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