SOLUTION: Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 9) 4(4x - 15) = 16x - 60 10) 9x + 2x = 10x 11) -4(x + 6) + 165 = 5x - 9(x - 9

Algebra ->  Equations -> SOLUTION: Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 9) 4(4x - 15) = 16x - 60 10) 9x + 2x = 10x 11) -4(x + 6) + 165 = 5x - 9(x - 9      Log On


   

Question 1059133: Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
9) 4(4x - 15) = 16x - 60
10) 9x + 2x = 10x
11) -4(x + 6) + 165 = 5x - 9(x - 9)
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try solving for x and find what happens.

#11 only.
-4%28x%2B6%29%2B165=5x-9%28x-9%29
-4x-20%2B165=5x-9x%2B81
-9x-145=-4x%2B81
-5x=145%2B81
-5x=226
x=-226%2F5--------Equation would be true if x=-226/5. Classify the way you need. Conditional is best and only meaningful choice.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
9) 4(4x - 15) = 16x - 60
10) 9x + 2x = 10x
11) -4(x + 6) + 165 = 5x - 9(x - 9)
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

9)  4(4x - 15) = 16x - 60  --->

    16x - 60 = -16x - 60,

    16x + 16x = -60 + 60

    32x = 0,

    x = 0.   <==== It is not an identity.  It is equation.  It is not inconsistent.  In opposite, it is consistent.


10)  9x + 2x = 10x  --->

     11x = 10x,

     11x - 10x = 0,

     x = 0.  <==== It is not an identity. It is equation.  It is not inconsistent.  In opposite, it is consistent.


11)  -4(x + 6) + 165 = 5x - 9(x - 9)  --->

     -4x - 24 + 165 = 5x - 9x + 81,

     -4x +141 = -4x + 81,  --->

     141 = 81.   <==== This equality is impossible.  Hence, the original equation is inconsistent.

Disregard what "josgarithmetic" wote in your post. It is wrong.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
9) 4(4x - 15) = 16x - 60
10) 9x + 2x = 10x
11) -4(x + 6) + 165 = 5x - 9(x - 9)
highlight_green%28matrix%281%2C4%2C+%229%29%22%2C+0%2C+%22=%22%2C+0%29%29 --------- What type of equation is it when this happens? You need to answer that!

highlight_green%28matrix%281%2C4%2C+%2210%29%22%2C+x%2C+%22=%22%2C+0%29%29 -------- What type of equation is it when this happens? You need to answer that!

highlight_green%28matrix%281%2C4%2C+%2211%29%22%2C+0%2C+%22+%22%3C%3E%22+%22%2C+-+60%29%29 ---- What type of equation is it when this happens? You need to answer that!