SOLUTION: Can someone help me solve and graph this inequality problem? -21 &#8804; 4x +3 and 4x +3 < 23

Algebra ->  Inequalities -> SOLUTION: Can someone help me solve and graph this inequality problem? -21 &#8804; 4x +3 and 4x +3 < 23      Log On


   

Question 460087: Can someone help me solve and graph this inequality problem?
-21 ≤ 4x +3 and 4x +3 < 23
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, solve the inequalities separately.

Let's solve the first inequality -21%3C=4x%2B3


-21%3C=4x%2B3 Start with the given inequality.


0%3C=4x%2B3%2B21 Add 21 to both sides.


-4x%3C=3%2B21 Subtract 4x from both sides.


-4x%3C=24 Combine like terms on the right side.


x%3E=%2824%29%2F%28-4%29 Divide both sides by -4 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E=-6 Reduce.


So the solution to the first inequality is x%3E=-6

-----------------------------------------------

Now let's solve the second inequality 4x%2B3%3C23


4x%2B3%3C23 Start with the given inequality.


4x%3C23-3 Subtract 3 from both sides.


4x%3C20 Combine like terms on the right side.


x%3C%2820%29%2F%284%29 Divide both sides by 4 to isolate x.


x%3C5 Reduce.


So the solution to the second inequality is x%3C5

===============================================================

So the two solutions are x%3E=-6 AND x%3C5

So the question is now: what number(s) fall are BOTH greater than -6 AND less than 5? The answer is any number that satisfies the compound inequality -6%3C=x%3C5. Basically, I combined the two inequalities above to form the final compound inequality.


So the answer is -6%3C=x%3C5