SOLUTION: Hi, I've tried solving this equation in multiple ways but can't seem to crack it. The problem is 2/3 (3x+9)=-2(2x+6), please show me the steps to solve as well, Thanks much ;)

Algebra ->  Linear-equations -> SOLUTION: Hi, I've tried solving this equation in multiple ways but can't seem to crack it. The problem is 2/3 (3x+9)=-2(2x+6), please show me the steps to solve as well, Thanks much ;)      Log On


   

Question 1203510: Hi, I've tried solving this equation in multiple ways but can't seem to crack it. The problem is 2/3 (3x+9)=-2(2x+6), please show me the steps to solve as well, Thanks much ;)
Found 3 solutions by MathLover1, josgarithmetic, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
2/3 (3x+9)=-2(2x+6)

You mean this way>
%282%2F3%29%283x%2B9%29=-2%282x%2B6%29

Multipl. bth. sides 3
2%283x%2B9%29=-6%282x%2B6%29
Distrib. prpty.
6x%2B18=-12x-36
Additive Inverse prop.
.
.
18x=-54

x=-3-------------------answer


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Looking closely, both sides of equation have a factor highlight_green%28x%2B3%29, which can very much make simplification at the start, easier.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


%282%2F3%29%283x%2B9%29=-2%282x%2B6%29

Nearly all resources will say to solve the equation by isolating the variable. But sometimes it is possible to reach the answer with less work if we don't do that.

In this problem, first simplify the expression on the left:

%282x%2B6%29=-2%282x%2B6%29

Now "2x+6" is a common expression on both sides, so....

%282x%2B6%29%2B2%282x%2B6%29=0
3%282x%2B6%29=0
3=0 (never!) or 2x%2B6=0
2x=-6
x=-3