What is the solution of 3 times the absolute value of x plus 5 is less than or equal to 6?

Question

anonymous · Answer

ok so write the equation out
$$3|x+5|\le6$$

anonymous · Answer

divide both sides by 3 (which is positive so keep the sign)

anonymous · Answer

$$|x+5|\le2$$

anonymous · Answer

The final step is understanding what it means. So you want values of x such that the magnitude PLUS 5 is less than or equal to 2. This means that x must be constrained between -3 and -7. We to set it up so that x+5<2 AND x+5<-2

anonymous · Answer

@sylbot thanks again

anonymous · Answer

oh btw those should be $$\le $$ signs sorry I forgot.

anonymous · Answer

oopsoops I made a mistake.

anonymous · Answer

the constraint should be $$-7 \le x \le -3$$

anonymous · Answer

sorry about that, I mess up the signs