3x+2 ≤ -7 or -2x+1 ≤ 9 this is an interval problem. Would the answer be [-3,-4] or (- infinety,-3]∪ [-4,+infinety)?

Question

3x+2 ≤ -7 or -2x+1 ≤ 9 this is an interval problem.  Would the answer be [-3,-4] or (- infinety,-3]∪  [-4,+infinety)?

anonymous · Answer

Just a sec.

anonymous · Answer

okay

anonymous · Answer

Lets solve the first guy. First you can subtract 2 from both sides:
$$3x \le-9$$

anonymous · Answer

so $$x \le-3$$

anonymous · Answer

xyup

anonymous · Answer

So from negative infinity, up to and including -3, this solution is satisfied.

anonymous · Answer

Since x is less than -3, it is going to the left on the number line (towards minus infinity)

anonymous · Answer

So the solution would be (-infinity,-3]

anonymous · Answer

Always remember that you use parenthesis on infinities, and since we are including -3, we can have a square bracket.

anonymous · Answer

okay

anonymous · Answer

Solving the other one, we get $$x \ge -4$$

anonymous · Answer

So now we want to start at -4 on the number line, include it, and have anything greater than it be a solution (anything to the right of -4 on the number line...so out towards positive infinity)

anonymous · Answer

So its solution would be $$[-4,\infty)$$

anonymous · Answer

thanks i didn't know which way to go with it lol

anonymous · Answer

If you want to union the two, the entire solution would be ($$(-\infty,-3] \cup [-4, \infty)$$

anonymous · Answer

Assuming they are solutions to the same system

anonymous · Answer

Yup, no problem.