SOLUTION: In order for the equation below to have infinitely many solutions, what must the value of m be? mx + 3(mx – 12) + 14 = 11(x – 2) + 5x

Algebra ->  Inequalities -> SOLUTION: In order for the equation below to have infinitely many solutions, what must the value of m be? mx + 3(mx – 12) + 14 = 11(x – 2) + 5x       Log On


   

Question 921010: In order for the equation below to have infinitely many solutions, what must the value of m be?
mx + 3(mx – 12) + 14 = 11(x – 2) + 5x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If you solve an equation and get to an absolute truth (a statement not involving variables that is true), you have infinitely many solutions.
Example:
If you solve this you get:
x+%2B+5+=+x+%2B+5
5+=+5+ which is an absolute truth (a statement not involving variables that is true)
so, solve your equation for m:
mx+%2B+3%28mx+-12%29+%2B+14+=+11%28x+-2%29+%2B+5x
mx+%2B+3mx+-36+%2B+14+=+11x+-22+%2B+5x

mx+%2B+3mx+-+cross%2822%29+=+16x+%96cross%2822%29
%28m+%2B+3m%29cross%28x%29++=+16cross%28x%29+
4m++=+16+
m++=+16%2F4+
m++=+4+

check if we get an absolute truth (a statement not involving variables that is true) if we plug in m++=+4+

4x+%2B+3%284x+-12%29+%2B+14+=+11%28x-2%29+%2B+5x
4x+%2B+12x+-36+%2B+14+=+11x+-22+%2B+5x
16x+-22+=+16x+%96+22+
16x++=+16x++
16x-16x+=0+
0+=0+
line 4x+%2B+3%284x-12%29
+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+4x+%2B+3%284x-12%29+%2B+14+%29+
line +11%28x+-2%29+%2B+5x

+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C++11%28x+-2%29+%2B+5x+%29+
together,4x+%2B+3%284x-12%29=11%28x+-2%29+%2B+5x
+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C16x+%2C+16x++%29+
as you can see two lines are directly on top of each other