Answer:
The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is (-∞,2] ∪ [8,∞)
Step-by-step explanation:
When solving absolute value inequalities, there are two cases to consider.
Case 1: The expression within the absolute value symbols is positive.
Case 2: The expression within the absolute value symbols is negative.
The solution is the intersection of the solutions of these two cases.
In other words, for any real numbers a and b,
- if |a|> b then a>b or a<-b
- if |a|< b then a<b or a>-b
So, being |3x-9|≤15
Solving: 3x-9 ≤ 15
3x ≤15 + 9
3x ≤24
x ≤24÷3
x≤8
or 3x-9 ≥ -15
3x ≥-15 +9
3x ≥-6
x ≥ (-6)÷3
x ≥ -2
The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]
So, being |2x-3|≥5
Solving: 2x-3 ≥ 5
2x ≥ 5 + 3
2x ≥8
x ≥8÷2
x≥8
or 2x-3 ≤ -5
2x ≤-5 +3
2x ≤-2
x ≤ (-2)÷2
x ≤ -2
Expressing the solution as an interval: (-∞,2] ∪ [8,∞)
⓵ You need to solve the left side first in order to isolate the × and find it’s value :
-7× + 6 = 27
-6 -6
↓
-7× = 21
÷-7 ÷-7
↓
× = -3
If you find it too difficult to divide a number by a negative, just divide 21 by 7 and always remember that when dividing, when the signs are different the answer is negative. So knowing that you could just divide 21 by 7, which is 3, and add a negative sign in front!
I hope this helped, if there’s anything let me know! ☻
Possible Answer:
Millimeter.
Step-by-step explanation:
Judging by the item in the question, a straw, millimeter is probably the correct measurement of the width of it.
