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.______
Q. 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.______
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.−(s+1)>2−s−1>2−s>2+1−s>3Now, we multiply both sides by −1, remembering to reverse the inequality sign because we are multiplying by a negative number.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:s<−3 or s>1
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