Solve for s.∣s−6∣>8Write 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−6∣>8Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.______
Split Inequalities: We have the absolute value inequality ∣s−6∣>8. We need to split this into two separate inequalities because the absolute value of a number is greater than 8 if the number itself is either greater than 8 or less than −8.So, we have two cases:1. s−6>82. s−6<−8
Solve First Inequality: Solve the first inequality s−6>8. Add 6 to both sides to isolate s: s−6+6>8+6s>14
Solve Second Inequality: Solve the second inequality s−6<−8. Add 6 to both sides to isolate s: s−6+6<−8+6s<−2
Combine Inequalities: Combine the two inequalities into a compound inequality.The solution to the original inequality ∣s−6∣>8 is s<−2 or s>14.
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