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Solve for $c$ . $|{-4c}| > 4$ 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.

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Solve absolute value inequalities

Full solution

Q. Solve for

c

.

|{-4c}| > 4

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.

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 $c > 1$

More problems from Solve absolute value inequalities

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