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Solve for $q$ . $\newline$ $|2q| = 6$ $\newline$ 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

|2q| = 6

\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 $|2q| = 6$ means that the absolute value of $2q$ is equal to $6$ . This implies that $2q$ can either be $6$ or $-6$ because the absolute value of a number is always non-negative.
Set up separate equations: Set up two separate equations to solve for $q$ . Since $|2q|$ can be either $6$ or $-6$ , we can write two equations: $1$ ) $2q = 6$ $2$ ) $2q = -6$
Solve first equation for q: Solve the first equation for $q$ . $\newline$ Divide both sides of the equation $2q = 6$ by $2$ to isolate $q$ . $\newline$ $q = \frac{6}{2}$ $\newline$ $q = 3$
Solve second equation for q: Solve the second equation for q. $\newline$ Divide both sides of the equation $2q = -6$ by $2$ to isolate $q$ . $\newline$ $q = -6 / 2$ $\newline$ $q = -3$

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\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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Question

\$200

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\newline

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\newline

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