Exercise
Solve the inequality:
2(x+3)+x\leq 4x+6<x+7
Final Answer
Solution
2(x+3)+x\leq 4x+6<x+7
Split the dual inequality into two inequalities:
2(x+3)+x\leq 4x+6
4x+6<x+7
Solve the first inequality:
2(x+3)+x\leq 4x+6
2x+6+x\leq 4x+6
2x+4x+x\leq -6+6
7x\leq 0
x\leq 0
Solve the second inequality:
4x+6<x+7
4x-x<7-6
3x<1
x<\frac{1}{3}
Finally, intersect both results:
x\leq 0
and
x<\frac{1}{3}
Therefore, final answer is
0\leq x<\frac{1}{3}
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