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Inequalities – dual inequality with one variable – Exercise 5690

Exercise

Solve the inequality:

2(x+3)+x\leq 4x+6<x+7

Final Answer


0\leq x<\frac{1}{3}

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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