Solve for q. |-7q| > 7 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Identify Inequality: We have the inequality: |-7q| > 7 First, we solve for |-7q|. |-7q| > 7 means that the absolute value of -7q is greater than 7.Split into Two: The absolute value inequality |-7q| > 7 can be split into two separate inequalities because if the expression inside the absolute value is positive, it must be greater than 7, and if it's negative, its opposite must be greater than 7. So we have: -7q > 7 or -7q 7 We divide both sides by -7, remembering to flip the inequality sign because we are dividing by a negative number: q 1Combine Inequalities: Combining both inequalities, we get the compound inequality: q 1 This is the solution to the original problem.

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Solve for $q$ . $\newline$ |-7q| > 7 $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form. $\newline$ ______

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Algebra 2

Solve absolute value inequalities

Full solution

Q. Solve for

q

\newline

|-7q| > 7

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

______

Identify Inequality: We have the inequality: $\newline$ |-7q| > 7$\newlineFirst, we solve for \$|-7q|$.$\newline$$|-7q| > 7$ means that the absolute value of $-7q$ is greater than $7$.
Split into Two: The absolute value inequality $|-7q| > 7$ can be split into two separate inequalities because if the expression inside the absolute value is positive, it must be greater than $7$, and if it's negative, its opposite must be greater than $7$. So we have:$\newline$$-7q > 7$ or $-7q < -7$
Solve First Inequality: Now we solve each inequality separately. For the first inequality:$\newline$$-7q > 7$$\newline$We divide both sides by $-7$, remembering to flip the inequality sign because we are dividing by a negative number:$\newline$$q < -1$
Solve Second Inequality: For the second inequality:$\newline$$-7q < -7$$\newline$We again divide both sides by $-7$, flipping the inequality sign:$\newline$$q > 1$
Combine Inequalities: Combining both inequalities, we get the compound inequality:$\newline$$q < -1$ or $q > 1$$\newline$This is the solution to the original problem.