Question

List the integers in each solution set. 2 ≤2x <x+5
how to do this step by step ?
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Answer 1

Step-by-step explanation:

By subtracting 2 from both sides, we get the equivalent inequality

x>−5 .

So, the solution set is

 x>−5 .

Answer 2

Answer: {1, 2, 3, 4}

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Step-by-step explanation:

The tri-inequality A < B < C breaks up into A < B and B < C

Use this idea to break up 2 ≤ 2x < x+5 into these two pieces

• 2 ≤ 2x
• 2x < x+5

We'll solve each inequality individually.

Let's start with the first one.

2 ≤ 2x

2/2 ≤ 2x/2

1 ≤ x

Now onto the second inequality

2x < x+5

2x-x < x+5-x

x < 5

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From here recombine 1 ≤ x and x < 5 to get 1 ≤ x < 5

If x is an integer only, then the roster set of solutions that satisfy this inequality is {1, 2, 3, 4}. Notice 5 is not part of the solution set, but 1 is.

We can replace x with any of those items in bold to get a true statement.

For instance, let's replace x with 3.

1 ≤ x < 5 updates to 1 ≤ 3 < 5 which is true

Let's go back to the original tri-inequality and replace each x with 3. Then simplify each side.

2 ≤ 2x < x+5

2 ≤ 2*3 < 3+5

2 ≤ 6 < 8

We end up with a true statement, which verifies that x = 3 is one of the integer solutions. I'll let you verify the other values 1,2, and 4.