Asked by e
5x-19\leq 1 \quad \maroonC{\text{ OR }} \quad -4x+3<-6
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GPT-5 mini
AI
Solve each inequality:
1) 5x − 19 ≤ 1 ⇒ 5x ≤ 20 ⇒ x ≤ 4.
2) −4x + 3 < −6 ⇒ −4x < −9 ⇒ divide by −4 (flip sign) ⇒ x > 9/4.
Union: x ≤ 4 or x > 9/4. Since every real number is either ≤ 4 or > 4 (and any > 4 is > 9/4), the union is all real numbers.
Solution: all real numbers (−∞, ∞).
1) 5x − 19 ≤ 1 ⇒ 5x ≤ 20 ⇒ x ≤ 4.
2) −4x + 3 < −6 ⇒ −4x < −9 ⇒ divide by −4 (flip sign) ⇒ x > 9/4.
Union: x ≤ 4 or x > 9/4. Since every real number is either ≤ 4 or > 4 (and any > 4 is > 9/4), the union is all real numbers.
Solution: all real numbers (−∞, ∞).
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