Question

Solve 6x + 3 < x < 3x + 9 for integers values of x

Answer 1

`\\ \sf\longmapsto 6x + 3 < x < 3x + 9 \\ \\ \sf\longmapsto 6x - 3x < x < 9 - 3 \\ \\ \sf\longmapsto 3x < x < 6 \\ \\ \sf\longmapsto x < (x)/(3) < 2`

Answer 2

-9/2 < x < -3/5

Explanation:

So first, we take the left part of the inequality to solve and ignore the right part for now, which leaves us 6x + 3 < x.

1. Subtract 3 from both sides:

6x < x - 3

2. subtract x from both sides:

5x < -3

3. divide 5 from both sides:

x < -3/5

Then, we do the same thing as part 1, but this time with x < 3x + 9.

1. Subtract 9 from both sides:

x - 9 < 3x

2. subtract x from both sides:

-9 < 2x

3. divide both sides by 2:

-9/2 < x.

Notice how we have a value that x is less than and a value that x is greater than. So now, all we have to do is to put the two inequalities together, leaving only one x in the middle. Hence, -9/2 < x < -3/5.

I hope this helped! :D