How do you know when to move the number to the left or the right.
For example
(x-5)/(x+8)=5/7 or
(y-2)/(y+2)=3/7
What are you trying to do? Solve for the unknown (x or y?)
First get rid of the fractions that have the unknowns in the denomimator. It is not a question of moving right or left.
In the first case,
7(x-5) = 5(x+8)
7x -35 = 5x + 40
2x = 75
x = 37.5
I know the first problems answer is 2/75 and the second is 5 and in both cases I seem to mess up on the last part of moving the numbers like for instance in the 2/75 I first had the answer of 75/2 I had the numbers right but the wrong placement and the same with the other I first had 4/20 instead of 20/4 which equals 5 so I need to know how do you know which way to move the number to the left or the right?
To determine when to move a number to the left or right in an equation, you need to isolate the variable on one side of the equation.
Let's take the first example: (x-5)/(x+8)=5/7
Step 1: Multiply both sides of the equation by the denominators of the fractions. In this case, multiply both sides by (x+8) and 7.
7(x-5) = 5(x+8)
Step 2: Distribute the multiplication on both sides of the equation.
7x - 35 = 5x + 40
Step 3: Move all terms containing the variable, in this case, x, to one side of the equation, and the constant terms to the other side.
Subtract 5x from both sides:
7x - 5x = 40 + 35
2x = 75
Step 4: Finally, divide both sides of the equation by the coefficient of the variable to solve for x.
2x/2 = 75/2
x = 37.5
In this case, we moved the variable terms (5x and 7x) to the left side of the equation and the constant terms (35 and 40) to the right side of the equation. This allowed us to isolate the variable and solve for x.
You can follow similar steps for the second example: (y-2)/(y+2)=3/7.