Well, let's first solve each equation:
1.) -4x + 6 - 3x = 12 - 2x - 3x
To start, combine each like-term on each side of the equal sign (The numbers with variables in-common // the numbers alike on the same side of the equal sign):
-7x + 6 = 12 - 5x
Now, we get the two terms with variables attached to them, on the same side, so, we do the opposite of subtraction, which is, addition:
-7x + 6 = 12 - 5x
+5x +5x
_____________
-2x + 6 = 12
Next, you do the opposite of addition, which is, subtraction, and, subtract 6 from both sides:
-2x + 6 = 12
-6 -6
____________
-2x = 6
Finally, divide by -2 on each side, to find out what the value of 'x' is:
-2x = 6
÷-2 ÷-2
________
x = -3
So, the answer is not 'A.'
_________________________________________
Now, we test out the rest of the equations, the exact same way:
2.) 4x + 6 + 3x = 12 + 2x + 3x
Combine your like-terms, on each side of the equal sign:
7x + 6 = 12 + 5x
Now, get both terms, with the variable, 'x,' to the same side, and, to do that, do the opposite of addition, which is, subtraction:
7x + 6 = 12 + 5x
-5x -5x
______________
2x + 6 = 12
Next, subtract 6 from both sides:
2x + 6 = 12
-6 -6
__________
2x = 6
Finally, divide by 2, on both sides:
2x = 6
÷2 ÷2
__________
x = 3
So, the answer is 'B.'
_________________________________________
3.) 4x + 6 - 3x = 12 - 2x - 3x
Again, we combine the like-terms, on both sides of the equal sign:
x + 6 = 12 - 5x
Now, we get both terms with the variable 'x,' to the same side, and, the opposite of subtraction, is addition, so, we're going to add 5x to both sides:
x + 6 = 12 - 5x
+ 5x + 5x
______________
6x + 6 = 12
Now, we subtract 6 from each side, because, the opposite of addition, is subtraction:
6x + 6 = 12
- 6 - 6
_____________
6x = 6
Now, divide by 6, on both sides:
6x = 6
÷ 6 ÷ 6
_____________
x = 1
So, the answer is not 'C.'
_________________________________________
4.) 4x + 6 - 3x = 12x + 2x + 3x
First, we combine the like-terms:
x + 6 = 17x
Next, we get both terms, with the variable, 'x,' to the same side:
x + 6 = 17x
-x -x
_____________
6 = 16x
Now, divide by 16, on both sides:
X = 3/8
So, 'D,' is not the answer.
_______________________
The answer is, 'B.'
I hope this helps!
One way to approach this problem is to go ahead and find the actual equation in slope-intercept form.
The slope of the line thru (3,6) and (5,4) is m = (6-4) / (3-5), or -2/2, or -1.
Subbing the known values of m, x and y, we get:
4 = -(5) + b. Then b = 9.
The correct equation (representing the data values in the table) is y = -x + 9.
Hey there! I'm happy to help!
Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.
We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.
If the line we are looking for is flat; it stays at the same y-value the entire time. We see that the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.
I hope that this helps! Have a wonderful day!
