SOLUTION: 7(x � 3) > 5x

SOLUTION: 7(x � 3) > 5x - 14

Question 77017: 7(x � 3) > 5x - 14
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
7(x � 3) > 5x - 14
.
The object of solving an inequality is to solve for x.
.
You can treat these problems about the same as an equation with one exception. That
exception is that if you divide or multiply both sides of the inequality by a negative
number, then you must reverse the direction of the inequality arrow.
.
Let's proceed. First multiply out the left side to get:
.
7x - 21 > 5x - 14
.
Get rid of the -21 on the left side of the equation by adding +21. But if you add + 21 to
the left side you must also add +21 to the right side. When you do that, the inequality
becomes:
.
7x > 5x + 7
.
(The +7 comes from -14 + 21.)
.
Now eliminate the 5x on the right side by subtracting 5x from it. But when you subtract
5x from the right side, you must also subtract it from the left side. This causes
the inequality to become:
.
2x > +7
.
Finally, divide both sides by 2 to solve for +x. That division causes the inequality
to become
.
x > +7/2 or x > +3.5
.
So x must lie to the right of 3.5 on the number line.
.
Let's spot check. Suppose we let x = +4. Plug that into the original problem and you
get:
.
7(4 � 3) > 5*4 - 14
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This simplifies to:
.
7(1) > 20 - 14
.
Which further simplifies to:
.
7 > 6
.
That works. Now suppose we let x be a number less that 3.5 ... say x = 3. Plug that
value into the original problem and it becomes:
.
7(3 � 3) > 5*3 - 14
.
which simplifies to:
.
0 > 15 - 14 or 0 > 1
.
that does NOT work. So from these couple of spot checks, it appears that our solution
is probably correct. (It is correct ...)
.
Hope this helps you to understand inequalities a little better, and helps you to see that
for the most part you can operate on them just as you would an equation. And don't forget
the rule that if you multiply or divide both sides of an inequality by a negative
quantity, you must reverse the direction of the inequality arrow. We did not need to
apply that rule in this problem.
.

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