9514 1404 393
Answer:
x > 5/3
Step-by-step explanation:
In general, inequalities are solved the same way that equations are: undo what is done to the variable. (Whatever you do to one side of the inequality, you must also do to the other side.)
If you were to evaluate this inequality for some value of x, you would ...
When solving for x, you undo these operations in reverse order. You undo the "subtract 5" by doing "add 5" <em>to both sides</em> of the inequality:
3x -5 +5 > 0 +5
3x > 5
You undo the "multiply by 3" by doing "divide by 3" <em>to both sides</em> of the inequality:
(3x)/3 > 5/3
x > 5/3 . . . . . . . the solution
__
<em>Additional comment</em>
The only difference between solving an equation and solving an inequality is that <em>multiplication or division by a negative number reverses the comparison symbol</em>.
Consider -1 > -2. When this is multiplied by -1, it becomes 1 < 2, with the comparison reversed.
__
As you can see, as long as multiplication and division are with positive numbers, the actual comparison symbol doesn't matter:
3x -5 > 0 ⇒ x > 5/3
3x -5 = 0 ⇒ x = 5/3
3x -5 < 0 ⇒ x < 5/3
