SOLUTION: solve 8x-5+9x=17x-5. Describe the type of answer if applicable

Question 91076: solve 8x-5+9x=17x-5. Describe the type of answer if applicable
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
8x - 5 + 9x = 17x - 5
.
Notice that on the left side you can combine the two terms that contain x. 8x + 9x equals 17x.
.
When you make that change the equation becomes:
.
17x - 5 = 17x - 5
.
Notice that the left side of this equation is identical to the right side. Because of
this reason, this type of equation is called an identity. Whatever value you wish to choose
for x, the given equation will always be true.
.
For example, in the given equation if you substitute 10 for x the equation becomes:
.
8(10) - 5 + 9(10) = 17(10) - 5
.
and this simplifies to:
.
80 - 5 + 90 = 170 - 5
.
which further reduces to:
.
165 = 165
.
Now try a different value for x. Suppose you choose x = 0. The equation becomes:
.
8(0) - 5 + 9(0) = 17(0) - 5
.
and this reduces to:
.
-5 = -5
.
Finally, let's choose x = -4. Substituting this value for x in the given equation
gives:
.
8(-4) - 5 + 9(-4) = 17(-4) - 5
.
Doing the multiplications results in:
.
-32 - 5 - 36 = -68 - 5
.
and combining the terms on the left and right sides:
.
-73 = -73
.
This should give you the idea of what an identity means. Our examples show that no matter
what value we tried for x, both sides of the given equation were equal.
.
Hope this clarifies the problem for you.
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