Solve for s. |s + 1| > 2 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Define Inequality: We have the inequality |s + 1| > 2. To solve for s, we need to consider the two cases that arise from the definition of absolute value: one where the expression inside the absolute value is positive, and one where it is negative.Positive Case: First, let's consider the case where the expression inside the absolute value is positive. This means we are looking at s + 1 > 2. To solve for s, we subtract 1 from both sides of the inequality. s + 1 - 1 > 2 - 1 s > 1Negative Case: Now, let's consider the case where the expression inside the absolute value is negative. This means we are looking at -(s + 1) > 2. To solve for s, we first distribute the negative sign and then add 1 to both sides of the inequality. -(s + 1) > 2 -s - 1 > 2 -s > 2 + 1 -s > 3 Now, we multiply both sides by -1, remembering to reverse the inequality sign because we are multiplying by a negative number. s 2. The compound inequality is: s 1

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Solve for $s$ .|s + 1| > 2Write 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 2

Solve absolute value inequalities

Full solution

Q. Solve for

s

|s + 1| > 2

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

______

Define Inequality: We have the inequality |s + 1| > 2. To solve for $s$ , we need to consider the two cases that arise from the definition of absolute value: one where the expression inside the absolute value is positive, and one where it is negative.
Positive Case: First, let's consider the case where the expression inside the absolute value is positive. This means we are looking at s + 1 > 2. To solve for $s$ , we subtract $1$ from both sides of the inequality.s + 1 - 1 > 2 - 1s > 1
Negative Case: Now, let's consider the case where the expression inside the absolute value is negative. This means we are looking at -(s + 1) > 2. To solve for $s$ , we first distribute the negative sign and then add $1$ to both sides of the inequality. $\newline$ -(s + 1) > 2 $\newline$ -s - 1 > 2 $\newline$ -s > 2 + 1 $\newline$ -s > 3 $\newline$ Now, we multiply both sides by $-1$ , remembering to reverse the inequality sign because we are multiplying by a negative number. $\newline$ s < -3
Combine Cases: Combining the two cases, we have a compound inequality that represents all the solutions to the original inequality |s + 1| > 2. The compound inequality is: $\newline$ s < -3 or s > 1