Solve for y. |y - 3| ≥ 12 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Absolute Value Inequality: We have the inequality |y - 3| ≥ 12. The absolute value inequality means that the expression inside the absolute value can be either greater than or equal to 12 or less than or equal to -12.Case 1: Greater Than or Equal to 12: First, we consider the case where the expression inside the absolute value is greater than or equal to 12: y - 3 ≥ 12 Now, we solve for y by adding 3 to both sides of the inequality: y - 3 + 3 ≥ 12 + 3 y ≥ 15Case 2: Less Than or Equal to -12: Next, we consider the case where the expression inside the absolute value is less than or equal to -12: y - 3 ≤ -12 Again, we solve for y by adding 3 to both sides of the inequality: y - 3 + 3 ≤ -12 + 3 y ≤ -9Compound Inequality: Combining both cases, we get a compound inequality: y ≤ -9 or y ≥ 15 This is the solution to the given inequality.

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Solve for $y$ . $|y - 3| \geq 12$ 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 1

Solve absolute value inequalities

Full solution

Q. Solve for

y

|y - 3| \geq 12

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 $|y - 3| \geq 12$ . The absolute value inequality means that the expression inside the absolute value can be either greater than or equal to $12$ or less than or equal to $-12$ .
Case $1$ : Greater Than or Equal to $12$ : First, we consider the case where the expression inside the absolute value is greater than or equal to $12$ : $y - 3 \geq 12$ Now, we solve for $y$ by adding $3$ to both sides of the inequality: $y - 3 + 3 \geq 12 + 3$ $y \geq 15$
Case $2$ : Less Than or Equal to $-12$ : Next, we consider the case where the expression inside the absolute value is less than or equal to $-12$ : $\newline$ $y - 3 \leq -12$ $\newline$ Again, we solve for $y$ by adding $3$ to both sides of the inequality: $\newline$ $y - 3 + 3 \leq -12 + 3$ $\newline$ $y \leq -9$
Compound Inequality: Combining both cases, we get a compound inequality: $\newline$ $y \leq -9$ or $y \geq 15$ $\newline$ This is the solution to the given inequality.