3.
As written, the inequality has a negative coefficient for the variable n. It can be convenient to add the opposite of the right side of the inequality to both sides, so the comparison is to zero:
... 25 +3(4n -3) > 0
... 25 + 12n -9 > 0 . . . . . . eliminate parentheses using the distributive property
... 12n + 16 > 0 . . . . . . . . . collect terms
... n + 4/3 > 0 . . . . . . . . . . divide by 12*
... n > -4/3 . . . . . . . . . . . . add the opposite of the constant (first of answer choices)
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1.
6w -8 ≥ 22 . . . . . . . given
6w ≥ 30 . . . . . . . . . add 8
w ≥ 5 . . . . . . . . . . . .divide by 6* (second of answer choices)
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* When solving inequalities, solution can proceed in the same way it does for solving equations, with one exception. When multiplying or dividing by a negative number, the direction of the comparison changes. Consider the inequality
... 1 < 2
Now, see what happens when we multiply by -1:
... -1 > -2
You may note that we were always dividing by a positive number in the solutions above. That is intentional. In other words, we specifically chose the solution method for problem 3 so that we would avoid dividing by a negative number.
