Okay, so, to find out if an equation has one solution, an infinite number of solutions, or no solutions, we must first solve the equation:
(a) 6x + 4x - 6 = 24 + 9x
First, combine the like-terms on both sides of the equal sign:
10x - 6 = 24 + 9x
Now, we need to get the numbers with the variable 'x,' on the same side, by subtracting, in this case:
10x - 6 = 24 + 9x
-9x. -9x
______________
X - 6 = 24
Now, we do the opposite of subtraction, and add 6 to both sides:
X - 6 = 24
+6 +6
_________
X = 30
So, this particular equation has one solution.
(a). One solution
_____________________________________________________
(b) 25 - 4x = 15 - 3x + 10 - x
Okay, so again, we combine the like-terms, on the same side of the equal sign:
25 - 4x = 25 - 2x
Now, we get the 2 numbers with the variable 'x,' to the same side of the equal sign:
25 - 4x = 25 - 2x
+ 2x + 2x
________________
25 - 2x = 25
Next, we do the opposite of addition, and, subtract 25 on each side:
25 - 2x = 25
-25 -25
___________
-2x = 0
Finally, because we can't divide 0 by -2, this tells us that this has an infinite number of solutions.
(b) An infinite number of solutions.
__________________________________________________
(c) 4x + 8 = 2x + 7 + 2x - 20
Again, we combine the like-terms, on the same side as the equal sign:
4x + 8 = 4x - 13
Now, we get the 'x' variables on the same side, again, and, we do that by doing the opposite of addition, which, is subtraction:
4x + 8 = 4x - 13
-4x -4x
______________
8 = -13
Finally, because there is no longer an 'x' or variable, we know that this equation has no solution.
(c) No Solution
_________________________________
I hope this helps!
Answer:
02:3 and 12:18
Step-by-step explanation:
A proportion is formed when the larger ratio can be simplified to equal the smaller ratio:
#1
02:3 and 4:12
Reducing the larger ratio: 4:12=1:3
Hence, not a proportion.
#2
02:3 and 6:12
Reducing the larger ratio: 6:12=1:2
Hence, not a proportion.
#3
02:3 and 12:18
Reducing the larger ratio: 12:18=2:3
Hence, they form a proportion.
#4
02:3 and 12:18
Reducing the larger ratio: 12:36=1:3
Hence, not a proportion.
Answer:
see explanation
Step-by-step explanation:
Using the rules of exponents
•
⇔ 
•
= 1
•
×
⇔ 
Given
(a)
= 
(b)
= 3³
(c)
×
× 
=
× 1
= 
= 