Answer:
[tex]1\leq x<8[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]-3\leq6x-9<39[/tex]
First, note that this compound inequality is written in one, single inequality. Therefore, we can separate them into two and inequalities:
[tex]-3\leq 6x-9\text{ and } 6x-9<39[/tex]
Now, let's solve for both inequalities individually.
1)
We have:
[tex]-3\leq6x-9[/tex]
Add 9 to both sides. The right side cancels:
[tex]6\leq 6x[/tex]
Divide both sides by 6. The right side cancels:
[tex]1\leq x[/tex]
So, the solution for our first inequality is all numbers greater than or equal to 1.
2)
We have:
[tex]6x-9<39[/tex]
Add 9 to both sides:
[tex]6x<48[/tex]
Divide both sides by 6:
[tex]x<8[/tex]
So, our solution is all numbers less than 8.
All together, our solution is:
[tex]1\leq x\text{ and } x<8[/tex]
In words, this is: All numbers greater than or equal to 1 but less than 8.
So, our solution is all numbers between 1 and 8 including 1.
Therefore, we can write this as a compound inequality as follows:
[tex]1\leq x<8[/tex]
And this is our solution.
And we're done!
