Can someone please check this for mistakes please?
y=4(x+3)-2x
y=4x+3-2x
y=2x+3
2x+3=y
2x=y-3
x=y/2-3
Hopefully I have rearranged the formula y=4(x+3)-2x to express x in terms of y.
The first step is wrong
4(x+3) does not equal 4x + 3.
Y-4(X+3)-2X
Y=4X+12-2X
Y=2X+12
2X=Y-12
X=Y/2-6
To check if you have correctly rearranged the formula to express x in terms of y, we can substitute the expression you found for x back into the original formula and simplify.
Starting with your rearranged equation: x = y/2 - 3
Let's substitute this value of x back into the original equation y = 4(x + 3) - 2x:
y = 4((y/2 - 3) + 3) - 2(y/2 - 3)
Now, simplify the equation step by step:
y = 4((y/2 - 3) + 3) - 2(y/2 - 3)
= 4(y/2 - 3 + 3) - 2(y/2 - 3)
= 4(y/2) - 4(3) + 4(3) - 2(y/2) + 2(3)
= 2y - 12 + 12 - y + 6
= y - 6
So, we have y = y - 6.
This indicates that there might be a mistake in your rearrangement. I will now explain the correct method to rearrange the formula to express x in terms of y.
Original equation: y = 4(x+3) - 2x
Let's start by distributing 4 to x and 3:
y = 4x + 12 - 2x
Now, combine like terms by adding or subtracting:
y = 4x - 2x + 12
y = 2x + 12
To express x in terms of y, we can rearrange this equation:
2x + 12 = y
Subtract 12 from both sides:
2x = y - 12
Divide both sides by 2:
x = (y - 12) / 2
Therefore, the correct expression for x in terms of y is x = (y - 12) / 2.
Please double-check your work and make sure to follow these steps to rearrange the formula correctly.