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05/18/2024 · Middle School
Solve the following inequality using the addition principle and the multiplication principle \( 6(3 t+2)>3(11 t+11) \)
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Step-by-step Solution
Solve the equation \( 6(3t+2)>3(11t+11) \).
Solve the inequality by following steps:
- step0: Solve for \(t\):
\(6\left(3t+2\right)>3\left(11t+11\right)\)
- step1: Calculate:
\(18t+12=3\left(11t+11\right)\)
- step2: Calculate:
\(18t+12=33t+33\)
- step3: Move the expression to the left side:
\(18t+12-\left(33t+33\right)>0\)
- step4: Calculate:
\(-15t-21>0\)
- step5: Move the constant to the right side:
\(-15t>0+21\)
- step6: Remove 0:
\(-15t>21\)
- step7: Change the signs:
\(15t<-21\)
- step8: Divide both sides:
\(\frac{15t}{15}<\frac{-21}{15}\)
- step9: Divide the numbers:
\(t<-\frac{7}{5}\)
The solution to the inequality \(6(3t+2)>3(11t+11)\) using the addition principle and the multiplication principle is \(t<-\frac{7}{5}\).
Quick Answer
\(t<-\frac{7}{5}\)
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