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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Tutor-Verified Answer
Step-by-step Solution
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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