Solve for r.∣r∣+1≤13Write 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 r.∣r∣+1≤13Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.______
Isolate absolute value expression: First, we need to isolate the absolute value expression on one side of the inequality.∣r∣+1≤13Subtract 1 from both sides to isolate ∣r∣.∣r∣+1−1≤13−1∣r∣≤12
Consider absolute value definition: Now, we need to consider the definition of absolute value, which states that ∣r∣)isthedistanceof$r from 0 on the number line. This means that r can be either positive or negative, but not greater than 12 in magnitude.So we have two cases:1. r≤12 (when r is positive or zero)2. −r≤12 (when r is negative)
Solve for negative values: For the second case, we need to solve for r. To do this, we multiply both sides by −1, remembering to reverse the inequality sign because we are multiplying by a negative number.−r≤12(−1)(−r)≥(−1)(12)r≥−12
Combine both cases: Combining both cases, we get the compound inequality that represents all possible values of r.−12≤r≤12This inequality shows that r can be any number between −12 and 12, inclusive.
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