Solve for c. |-4c| > 4 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Identify Inequality: We have the inequality: |-4c| > 4 Solve for |-4c|. |-4c| > 4 This means that the absolute value of -4c is greater than 4.Split into Two: The absolute value inequality |-4c| > 4 can be split into two separate inequalities because if the expression inside the absolute value is positive, it must be greater than 4, and if it is negative, its opposite must be greater than 4. So we have two cases: -4c > 4 or -4c 4: Now we solve each inequality separately. First, we solve -4c > 4: -4c > 4 Divide both sides by -4, remembering to reverse the inequality sign because we are dividing by a negative number. c 1Combine Inequalities: Now we combine both inequalities to form the compound inequality. The solution to the original inequality |-4c| > 4 is: c 1

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Solve for $c$ .|{-4c}| > 4Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form.

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Algebra 2

Solve absolute value inequalities

Full solution

Q. Solve for

c

|{-4c}| > 4

Write a compound inequality like

1 < x < 3

or like

x < 1

x > 3

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

Identify Inequality: We have the inequality: $\newline$ |-4c| > 4 $\newline$ Solve for $|-4c|$ . $\newline$ |-4c| > 4 $\newline$ This means that the absolute value of $-4c$ is greater than $4$ .
Split into Two: The absolute value inequality |-4c| > 4 can be split into two separate inequalities because if the expression inside the absolute value is positive, it must be greater than $4$ , and if it is negative, its opposite must be greater than $4$ . $\newline$ So we have two cases: $\newline$ -4c > 4 or -4c < -4
Solve -4c > 4: Now we solve each inequality separately. $\newline$ First, we solve -4c > 4: $\newline$ -4c > 4 $\newline$ Divide both sides by $-4$ , remembering to reverse the inequality sign because we are dividing by a negative number. $\newline$ c < -1
Solve -4c < -4: Next, we solve -4c < -4: $\newline$ -4c < -4 $\newline$ Again, divide both sides by $-4$ , reversing the inequality sign. $\newline$ c > 1
Combine Inequalities: Now we combine both inequalities to form the compound inequality. $\newline$ The solution to the original inequality |-4c| > 4 is: $\newline$ c < -1 or c > 1