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

Isolate absolute value: We have the inequality |4z| > 4. To solve for z, we first isolate the absolute value expression on one side of the inequality. |4z| > 4Recognize absolute value inequality: Next, we recognize that the absolute value inequality |4z| > 4 means that the expression inside the absolute value, 4z, is either greater than 4 or less than -4. This is because the absolute value of a number is its distance from zero on the number line, so if the distance is greater than 4, the number itself could be either greater than 4 or less than -4. So we can write two separate inequalities: 4z > 4 or 4z 4 Divide both sides by 4 to isolate z: z > 1Solve second inequality: Now we solve the second inequality: 4z 1 or z 4.

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Solve for $z$ .|4z| > 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

z

|4z| > 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.

Isolate absolute value: We have the inequality |4z| > 4. To solve for $z$ , we first isolate the absolute value expression on one side of the inequality. $\newline$ |4z| > 4
Recognize absolute value inequality: Next, we recognize that the absolute value inequality |4z| > 4 means that the expression inside the absolute value, $4z$ , is either greater than $4$ or less than $-4$ . This is because the absolute value of a number is its distance from zero on the number line, so if the distance is greater than $4$ , the number itself could be either greater than $4$ or less than $-4$ . So we can write two separate inequalities: 4z > 4 or 4z < -4
Solve first inequality: Now we solve each inequality for $z$ . Starting with the first inequality: $\newline$ 4z > 4 $\newline$ Divide both sides by $4$ to isolate $z$ : $\newline$ z > 1
Solve second inequality: Now we solve the second inequality: $\newline$ 4z < -4 $\newline$ Divide both sides by $4$ to isolate $z$ : $\newline$ z < -1
Combine solutions: Combining the two solutions, we get the compound inequality for $z$ :z > 1 or z < -1This is the solution to the original inequality |4z| > 4.