Answer:
[-6 , 0]
Explanation:
If the absolute value of an expression is equal to a number, that means that the expression itself could be equal to either the negative equivalent to that number or the positive equivalent.
for example, if my inequality is |x| > -3
x could either be:
-3 or 3
So,
| 2(x - 1) + 8 | ≤ 6
can be separated into two separate inequalities:
2(x - 1) + 8 ≤ 6
or, 2(x - 1) + 8 ≥ - 6
we solve these inequalities separately.
2(x - 1) + 8 ≤ 6
2x - 2 + 8 ≤ 6 [distribute 2]
2x ≤ 0 [add 2 to both sides, subtract 8 from both sides]
x ≤ 0 [finalize isolating x by dividing both sides of the equation by 2]
expressed as [in interval notation]:
(-∞, 0]
now, let's solve for the other inequality.
2(x - 1) + 8 ≥ - 6
2x - 2 + 8 ≥ - 6 [distribute 2]
2x ≥ -12 [add 2 to both sides, subtract 8 from both]
x ≥ -6 [divide both by 2 to isolate x]
expressed as [in interval notation]:
[-6 , ∞)
So, our answer for x is going to be
-6 ≤ x ≤ 0
or, expressed in interval notation:
[-6 , 0]
*[ includes number]
*( is not equal to number)