Last qustion of the ! show work plz and !

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!