Schneider Young
01/29/2023 · Primary School

Solve for \( a \) \( \frac{a-2}{3}>a+4 \) \( a>-7 \) \( a<-7 \) \( a>\frac{5}{2} \) \( a<-5 \)

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Solve the equation \( \frac{a-2}{3}>a+4 \). Solve the inequality by following steps: - step0: Solve for \(a\): \(\frac{a-2}{3}>a+4\) - step1: Multiply both sides: \(\frac{a-2}{3}\times 3>\left(a+4\right)\times 3\) - step2: Multiply the terms: \(a-2>3a+12\) - step3: Move the variable to the left side: \(a-2-3a>12\) - step4: Subtract the terms: \(-2a-2>12\) - step5: Move the constant to the right side: \(-2a>12+2\) - step6: Add the numbers: \(-2a>14\) - step7: Change the signs: \(2a<-14\) - step8: Divide both sides: \(\frac{2a}{2}<\frac{-14}{2}\) - step9: Divide the numbers: \(a<-7\) The solution to the inequality \( \frac{a-2}{3}>a+4 \) is \( a<-7 \). Given the additional conditions: - \( a>-7 \) - \( a<-7 \) - \( a>\frac{5}{2} \) - \( a<-5 \) We can see that the only condition that satisfies all the given conditions is \( a<-7 \).

Quick Answer

The solution is \( a<-7 \).
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