***Inverse of mult. by 10 is div. both sides
by 10**

If you put -2 back in for *x* in the original
problem you will see that **-2 is the solution we are looking for.**

***Inverse of add. 5 is sub. 5**

***Inverse of mult. by -1 is div. by -1**

If you put 7 back in for *x* in the original
problem you will see that **7 is the solution we are looking for.**

***Get all x terms
on one side**

***Inverse of sub. 16 is add. 16**

***Inverse of mult. by 4 is div. by 4**

If you put 5/2 back in for *x* in the original
problem you will see that **5/2 is the solution we are looking for.**

***Get all the x terms on one side**

Where did our variable, *x,* go???
It disappeared on us. Also note how we ended up with a FALSE statement,
-3 is not equal to -4. This does not mean that *x* = -3 or* x* = -4.

**Whenever your variable drops out AND you end
up with a FALSE statement, then after all of your hard work, there is NO
SOLUTION.**

So, **the answer is no solution which means this is an inconsistent
equation.**

***Get all the x terms on one side**

***Inverse of add. 2 is sub. 2**

***Inverse of mult. by -3 is div. by -3**

If you put 4/3 back in for *x *in the original
problem you will see that** 4/3 is the solution we are looking for.**

**This would be an example of a conditional equation, because we came
up with one solution.**

***Get all the x terms on one side**

Where did our variable, *x,* go???
It disappeared on us. Also note how we ended up with a TRUE statement,
-27 does indeed equal -27. This does not mean that *x* = -27.

**Whenever your variable drops out AND you end
up with a TRUE statement, then the solution is ALL REAL NUMBERS. **This
means that if you plug in any real number for *x* in this equation, the left side will equal the right side.

So **the answer is all real numbers, which means this equation is an
identity.**

Last revised on Dec. 16, 2009 by Kim Seward.

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