What equation is equivalent to 24=ax+4y-10, when solving for y?
A: y=7/2-ax/4
B: y=17/2-ax/4
C: y=17- ax/4
D: y=34- ax
24=ax+4y-10
34 - ax = 4y
y = (34-ax)/4 or 17/2 - ax/4 , looks like B
Well, let's solve this equation with a touch of humor!
To begin, let's isolate the term with y. To do that, we'll move the ax term and the constant term to the other side of the equation:
24 - ax - 4y = -10
Now, let's get rid of that 4 in front of the y by dividing through the equation by 4:
6 - (ax/4) - y = -10/4
Simplifying, we have:
6 - ax/4 - y = -5/2
Now, let's bring back the y term to the left side of the equation:
-ax/4 - y = -5/2 - 6
This simplifies to:
-ax/4 - y = -17/2
Lastly, let's get rid of that negative sign in front of the y by multiplying the entire equation by -1:
ax/4 + y = 17/2
And there you have it! After all the humor and simplification, we are left with the equation:
y = 17/2 - (ax/4)
So, the correct answer is B: y = 17/2 - (ax/4).
To solve for y, we need to isolate the term that contains y on one side of the equation.
Starting with the equation 24 = ax + 4y - 10, we can rearrange the terms as follows:
24 - ax + 10 = 4y
Combining like terms, we get:
34 - ax = 4y
Dividing both sides by 4, we have:
(34 - ax)/4 = y
So, the equation equivalent to 24 = ax + 4y - 10, when solving for y, is:
y = (34 - ax)/4
Therefore, the correct answer is option D: y = 34 - ax.
To solve for y in the equation 24 = ax + 4y - 10, you need to isolate the variable y on one side of the equation. Here's how you can do it step by step:
1. Start with the given equation: 24 = ax + 4y - 10.
2. Move the ax term to the other side of the equation by subtracting ax from both sides: 24 - ax = 4y - 10.
3. Combine the constant terms on the right side of the equation: 24 - ax = 4y - 10 + 10.
4. Simplify: 24 - ax = 4y.
5. Divide both sides of the equation by 4 to isolate y: (24 - ax)/4 = (4y)/4.
6. Simplify: (24 - ax)/4 = y.
So, the equation becomes y = (24 - ax)/4. Now let's compare this result with the answer choices:
A: y = 7/2 - ax/4 - This equation does not match the result we obtained.
B: y = 17/2 - ax/4 - This equation does not match the result we obtained.
C: y = 17 - ax/4 - This equation does not match the result we obtained.
D: y = 34 - ax - This equation does match the result we obtained.
Therefore, the equivalent equation, when solving for y, is y = 34 - ax. Hence, the correct answer is option D.