Question

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

Answer 1

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

Answer 2

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

Answer 3

\[|x+5|\le2\]

Answer 4

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

Answer 5

@sylbot thanks again

Answer 6

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

Answer 7

oopsoops I made a mistake.

Answer 8

the constraint should be \[-7 \le x \le -3\]

Answer 9

sorry about that, I mess up the signs