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

Absolute Value Inequality: We have the inequality: |-4v| ≤ 4 First, we solve for |-4v|. |-4v| ≤ 4 means that the absolute value of -4v is less than or equal to 4.Splitting into Two Inequalities: The absolute value inequality |-4v| ≤ 4 can be split into two separate inequalities because the absolute value of a number is the distance from zero, and it can be either positive or negative. So, we have -4v ≤ 4 and -4v ≥ -4.Solving -4v ≤ 4: Now, we solve the first inequality -4v ≤ 4. Divide both sides by -4 to isolate v. Remember that dividing by a negative number reverses the inequality sign. v ≥ -1Solving -4v ≥ -4: Next, we solve the second inequality -4v ≥ -4. Again, divide both sides by -4, and reverse the inequality sign. v ≤ 1Combining Inequalities: Combining both inequalities, we get the compound inequality: -1 ≤ v ≤ 1 This means that v is greater than or equal to -1 and less than or equal to 1.

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Solve for $v$ . $|{-4v}| \leq 4$ 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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Algebra 1

Solve absolute value inequalities

Full solution

Q. Solve for

v

|{-4v}| \leq 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.

Absolute Value Inequality: We have the inequality: $\newline$ $|-4v| \leq 4$ $\newline$ First, we solve for $|-4v|$ . $\newline$ $|-4v| \leq 4$ means that the absolute value of $-4v$ is less than or equal to $4$ .
Splitting into Two Inequalities: The absolute value inequality $|-4v| \leq 4$ can be split into two separate inequalities because the absolute value of a number is the distance from zero, and it can be either positive or negative. $\newline$ So, we have $-4v \leq 4$ and $-4v \geq -4$ .
Solving $-4v \leq 4$ : Now, we solve the first inequality $-4v \leq 4$ . $\newline$ Divide both sides by $-4$ to isolate $v$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $v \geq -1$
Solving $-4v \geq -4$ : Next, we solve the second inequality $-4v \geq -4$ . Again, divide both sides by $-4$ , and reverse the inequality sign. $v \leq 1$
Combining Inequalities: Combining both inequalities, we get the compound inequality: $\newline$ $-1 \leq v \leq 1$ $\newline$ This means that $v$ is greater than or equal to $-1$ and less than or equal to $1$ .