What is the solution of 3 times the absolute value of x + 5 <= 6
I think the answer is x <= - 3 and x >= -7
If I'm not right, could you tell me why?
3|x+5|<= 6
|3x+15|<= 6
-15 -15
|3x| <= -9
/3 /3
x <= -3
Yes, you are correct.
Thank you-I appreciate it- I posted another- could you just check it to make sure I got this concept.
3|x+5| ≤ 6
|x+5| ≤ 2
x+5 ≤ 2 AND -x-5 ≤ 2
x ≤ -3 AND -x ≤ 7
x ≤ -3 AND x ≥ -7
-7 ≤ x ≤ -3
Thank you
To solve the inequality 3|x + 5| <= 6, we need to isolate x.
First, let's split the inequality into two cases:
1) When x + 5 ≥ 0 (or x ≥ -5), we have 3(x + 5) ≤ 6.
2) When x + 5 < 0 (or x < -5), we have 3(-x - 5) ≤ 6.
In the first case, we simplify the inequality:
3(x + 5) ≤ 6
3x + 15 ≤ 6
3x ≤ 6 - 15
3x ≤ -9
x ≤ -3
In the second case, we simplify the inequality:
3(-x - 5) ≤ 6
-3x - 15 ≤ 6
-3x ≤ 6 + 15
-3x ≤ 21
x ≥ -7
Thus, the solutions for x are x ≤ -3 and x ≥ -7.
So, your answer is correct! The solution is x ≤ -3 and x ≥ -7.