Weber Cook
09/27/2023 · Primary School
2.- \( \frac{8-x}{3}-\frac{4}{7}<\frac{-4 x-6}{-6} \)
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Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( \frac{8-x}{3}-\frac{4}{7}<\frac{-4x-6}{-6} \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(\frac{8-x}{3}-\frac{4}{7}<\frac{-4x-6}{-6}\)
- step1: Divide the terms:
\(\frac{8-x}{3}-\frac{4}{7}<\frac{2x+3}{3}\)
- step2: Multiply both sides:
\(\left(\frac{8-x}{3}-\frac{4}{7}\right)\times 21<\frac{2x+3}{3}\times 21\)
- step3: Multiply the terms:
\(56-7x-12<14x+21\)
- step4: Simplify:
\(44-7x<14x+21\)
- step5: Move the variable to the left side:
\(44-7x-14x<21\)
- step6: Subtract the terms:
\(44-21x<21\)
- step7: Move the constant to the right side:
\(-21x<21-44\)
- step8: Subtract the numbers:
\(-21x<-23\)
- step9: Change the signs:
\(21x>23\)
- step10: Divide both sides:
\(\frac{21x}{21}>\frac{23}{21}\)
- step11: Divide the numbers:
\(x>\frac{23}{21}\)
La solución de la desigualdad \( \frac{8-x}{3}-\frac{4}{7}<\frac{-4x-6}{-6} \) es \( x>\frac{23}{21} \).
Quick Answer
La solución es \( x>\frac{23}{21} \).
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