40 =15
x x - 20 This is a three part question>> first find the lcd method of solving this equations, and the second ones about cross-multiplying method to solve this equations ,The next question asked would the cross- multiplying method work for all rational equations?? Explain.
I am guessing you are trying to type the equation
40/x = 15/(x-20)
The LCD is x(x-20_
so
40/x (x(x-20)) = 15/(x-20) (x(x-20))
40(x-20) = 15x
40x - 800 = 15x
25x = 800
x = 32
cross-multplying gets you directly to
40(x-20) = 15x
etc
Cross-multiplying only works if your equation contains a single term on the left and a single term on the right,
that is,
you have to add/subract the terms first if you have more than one.
In that case I simply multiply each term by the LCD, to get rid of my fractions.
(1)40 =15 (2) x - 20 (2 DIFFERENT EQUATIONS)????? help please!!!!
To solve the equation 40/x = 15/(x - 20), we can use both the Least Common Denominator (LCD) method and the cross-multiplying method.
First, let's look at the LCD method:
Step 1: Find the LCD of the fractions involved.
In this case, the fractions have denominators "x" and "x-20". To find the LCD, we need to factor the denominators.
- The factorization of "x" is simply "x".
- The factorization of "x-20" is "(x-20)".
Since the denominators are already factored, the LCD is "x(x - 20)".
Step 2: Multiply both sides of the equation by the LCD.
Multiply the left side by "x(x - 20)" and the right side by "x(x - 20)". The purpose is to eliminate the denominators.
40/x * x(x - 20) = 15/(x - 20) * x(x - 20)
The equation becomes:
40(x - 20) = 15x
Step 3: Simplify and solve the resulting equation.
Expand and simplify the left side of the equation:
40x - 800 = 15x
Move variables to one side and constants to the other:
40x - 15x = 800
25x = 800
Divide both sides by 25 to solve for x:
x = 800/25
x = 32
So, using the LCD method, we find that the solution to the equation is x = 32.
Now, let's move on to the cross-multiplying method:
Step 1: Cross multiply the fractions.
Cross-multiplication means multiplying the numerator of one fraction by the denominator of the other and vice versa.
For the equation 40/x = 15/(x - 20), we have:
40(x - 20) = 15x
Step 2: Simplify and solve the resulting equation.
Expand and simplify the left side of the equation:
40x - 800 = 15x
Move variables to one side and constants to the other:
40x - 15x = 800
25x = 800
Divide both sides by 25 to solve for x:
x = 800/25
x = 32
Again, using the cross-multiplying method, we find that the solution to the equation is x = 32.
Regarding whether the cross-multiplying method works for all rational equations, the answer is yes. The cross-multiplying method can be used to solve any equation where two fractions are set equal to each other. This method works because it applies the principle that the product of the means (the middle terms) in a proportion is equal to the product of the extremes (the outer terms).