Answer:
one solution, infinite solutions, no solution
Step-by-step explanation:
12x+9=8x+1=4x = 1 solution
12x+9=8x=1=4x
We move all terms to the left:
12x+9-(8x)=0
We add all the numbers together, and all the variables
4x+9=0
We move all terms containing x to the left, all other terms to the right
4x=-9
x=-9/4
x=-2+1/4
2(x-3)=10x-6-8x = infinite solutions
Simplifying
2(x + -3) = 10x + -6 + -8x
Reorder the terms:
2(-3 + x) = 10x + -6 + -8x
(-3 * 2 + x * 2) = 10x + -6 + -8x
(-6 + 2x) = 10x + -6 + -8x
Reorder the terms:
-6 + 2x = -6 + 10x + -8x
Combine like terms: 10x + -8x = 2x
-6 + 2x = -6 + 2x
Add '6' to each side of the equation.
-6 + 6 + 2x = -6 + 6 + 2x
Combine like terms: -6 + 6 = 0
0 + 2x = -6 + 6 + 2x
2x = -6 + 6 + 2x
Combine like terms: -6 + 6 = 0
2x = 0 + 2x
2x = 2x
Add '-2x' to each side of the equation.
2x + -2x = 2x + -2x
Combine like terms: 2x + -2x = 0
0 = 2x + -2x
Combine like terms: 2x + -2x = 0
0 = 0
Solving
0 = 0
5x+6=5x-4= no solutions
Simplifying
5x + -6 = 5x + -4
Reorder the terms:
-6 + 5x = 5x + -4
Reorder the terms:
-6 + 5x = -4 + 5x
Add '-5x' to each side of the equation.
-6 + 5x + -5x = -4 + 5x + -5x
Combine like terms: 5x + -5x = 0
-6 + 0 = -4 + 5x + -5x
-6 = -4 + 5x + -5x
Combine like terms: 5x + -5x = 0
-6 = -4 + 0
-6 = -4
Solving
-6 = -4
