4 over 3x -1 = 8 over 5x + 6
cross multiply
To cross multiply, we multiply the numerator of one fraction by the denominator of the other fraction.
Starting with the equation:
4/(3x - 1) = 8/(5x + 6)
We cross multiply by multiplying 4 by (5x + 6) and 8 by (3x - 1):
4(5x + 6) = 8(3x - 1)
20x + 24 = 24x - 8
To solve the equation (4/3x - 1) = (8/5x + 6) by cross-multiplication, perform the following steps:
1. Multiply the numerator (top) of the left-hand side fraction by the denominator (bottom) of the right-hand side fraction, and vice versa. This step is called cross-multiplication.
(4)(5x + 6) = (8)(3x - 1)
2. Simplify both sides of the equation using the distributive property.
20x + 24 = 24x - 8
3. Rearrange the equation so that the variable is on one side and the constant terms are on the other side. You can do this by adding or subtracting the same quantity from both sides.
20x - 24x = -8 - 24
4. Combine like terms.
-4x = -32
5. Divide both sides of the equation by -4 to isolate the variable.
x = -32 / -4
6. Simplify the right side of the equation.
x = 8
Thus, the solution to the equation is x = 8.
To solve the equation 4/(3x - 1) = 8/(5x + 6) by cross multiplication, you need to follow these steps:
Step 1: Cross Multiply
Multiply the numerator of the first fraction (4) by the denominator of the second fraction (5x + 6), and multiply the denominator of the first fraction (3x - 1) by the numerator of the second fraction (8).
(4) * (5x + 6) = (8) * (3x - 1)
Step 2: Simplify
Simplify both sides of the equation by performing the multiplication.
20x + 24 = 24x - 8
Step 3: Rearrange the equation
Rearrange the equation by isolating the variables on one side and the constants on the other side.
20x - 24x = -8 - 24
-4x = -32
Step 4: Solve for x
To solve for x, divide both sides of the equation by -4.
x = -32 / -4
x = 8
Therefore, the solution to the equation is x = 8.