Solve for p. |-3p| > 6 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Absolute Value Inequality: We have the inequality: |-3p| > 6 First, we solve for |-3p|. |-3p| > 6 means that the absolute value of -3p is greater than 6.Splitting Inequality: Since the absolute value of a number is always non-negative, we can split the inequality into two separate inequalities without the absolute value: -3p > 6 or -3p 6 Divide both sides by -3 to isolate p. Remember that dividing by a negative number reverses the inequality sign: p 2Combining Solutions: Combining both parts of the solution, we get the compound inequality: p 2 This is the final answer in the form of a compound inequality.

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Solve for $p$ . $\newline$ |-3p| > 6 $\newline$ 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

p

\newline

|-3p| > 6

\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

______

Absolute Value Inequality: We have the inequality: $\newline$ |-3p| > 6 $\newline$ First, we solve for $|-3p|$ . $\newline$ |-3p| > 6 means that the absolute value of $-3p$ is greater than $6$ .
Splitting Inequality: Since the absolute value of a number is always non-negative, we can split the inequality into two separate inequalities without the absolute value: $\newline$ -3p > 6 or -3p < -6
Solving First Inequality: Now we solve each inequality separately. Starting with the first one: $\newline$ -3p > 6 $\newline$ Divide both sides by $-3$ to isolate $p$ . Remember that dividing by a negative number reverses the inequality sign: $\newline$ p < -2
Solving Second Inequality: Next, we solve the second inequality: $\newline$ -3p < -6 $\newline$ Again, divide both sides by $-3$ , and reverse the inequality sign: $\newline$ p > 2
Combining Solutions: Combining both parts of the solution, we get the compound inequality: $\newline$ p < -2 or p > 2 $\newline$ This is the final answer in the form of a compound inequality.