Answer:
[-6,-3]
Step-by-step explanation:
So we have the compound inequality:
[tex]2x+7\leq x+4\leq 3x+16[/tex]
Let's solve for each of the inequalities:
1)
We have:
[tex]2x+7\leq x+4[/tex]
Subtract x from both sides:
[tex]x+7\leq 4[/tex]
Subtract 7 from both sides:
[tex]x\leq -3[/tex]
So that's one of our answers.
2)
We have:
[tex]x+4\leq 3x+16[/tex]
Subtract 3x from both sides:
[tex]-2x+4\leq 16[/tex]
Subtract 4 from both sides:
[tex]-2x\leq 12[/tex]
Divide both sides by -2. Since we're dividing by a negative, flip the sign:
[tex]x\geq -6[/tex]
Therefore, our entire answer is:
[tex]-6\leq x\leq -3[/tex]
This means all values in between -3 and -6 including -3 and -6.
In interval notation, this is:
[tex][-6,-3][/tex]
So, A is -6.
And B is -3.
And we're done :)
