9514 1404 393
Answer:
x > 56
Step-by-step explanation:
The place to begin is this: look at the given inequality to see where the variable is and what has been done to it.
Here, the variable is on the left. It is buried in an expression in parentheses and other stuff is added outside. If you were to evaluate this expression using the Order of Operations, the operations you would perform are ...
- subtract x from 8
- multiply the result by 1/3
- add 8 to that
So, to solve for x, you can "undo" these operations in the reverse order.
8 +1/3(8 -x) < -8 . . . . . given
1/3(8 -x) < -16 . . . . . . . subtract 8 to undo addition of 8
8 -x < -48 . . . . . . . . . . multiply by 3 to undo multiplication by 1/3
8 < -48 +x . . . . . . . . . . add x to undo the subtraction of x
56 < x . . . . . . . . . . . . add 48 to undo the subtraction of 48
The solution is ...
x > 56
_____
Additional comment
You can do anything you like to an equation or inequality, as long as you do the same thing to both sides. When we say "subtract 8" we mean "subtract 8 from both sides".
The only difference between solving equations and solving inequalities is that some operations will cause the order to be reversed. Chief among these is multiplication or division by a negative number. Consider ...
1 < 2
-1 > -2 . . . . multiply (or divide) by -1, reverses the order
