Question

What are the integer solutions to the inequality below?
2x < 3x + 2 < x + 6

Answer 1

Answer:

-2 < x < 2

Step-by-step explanation:

split into 2 equations, solve for x

Answer 2

the integer solutions to the inequality is

$-2<x<2$

Given :

we need to find the integer solution for the given inequality

$2x < 3x + 2 < x + 6$

To solve this inequality , we break the inequalities and solve each inequality for x. Lets break the inequality

$2x < 3x + 2 < x + 6\\ 2x < 3x + 2 \; and \; 3x + 2 < x + 6$

$2x < 3x + 2\\2x -2x< 3x-2x + 2\\0<x+2\\0-2<x+2-2\\-2<x\\x>-2$

Now solve the second inequality

$3x + 2 < x + 6\\3x-x + 2 < x-x + 6\\2x + 2 < + 6\\2x + 2-2 < + 6-2\\2x<4\\x<2$

So the solution is x>-2  and x<2

the integer solutions to the inequality is $-2<x<2$

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