MATH SOLVE

4 months ago

Q:
# Solve 1/2+1/2x=x^2-7x+10/4x by re-writing the equation as a proportion. Which proportion is equivalent to the original equation?

Accepted Solution

A:

Rewriting the equation as a proportion, we have

(1/2 * 2x/2x) + (1/2x * 2/2) = (x^2 - 7x + 10)/4x

(2x/4x) + (2/4x) = (x^2 - 7x + 10)/4x

Multiplying both sides of the equation by 4x to clear the denominators:

2x + 2 = x^2 - 7x + 10

We now have a new equation that is equivalent to the original equation:

x^2 - 9x + 8 = 0

We can also write the equation into its factored form:

(x - 8)(x - 1) = 0

Now we have a product of two expressions that is equal to zero, which means any x value that makes either (x - 8) or (x - 1) zero will make their product zero.

x - 8 = 0 => x = 8

x - 1 = 0 => x = 1

Therefore, our solutions are x = 8 and x = 1.

(1/2 * 2x/2x) + (1/2x * 2/2) = (x^2 - 7x + 10)/4x

(2x/4x) + (2/4x) = (x^2 - 7x + 10)/4x

Multiplying both sides of the equation by 4x to clear the denominators:

2x + 2 = x^2 - 7x + 10

We now have a new equation that is equivalent to the original equation:

x^2 - 9x + 8 = 0

We can also write the equation into its factored form:

(x - 8)(x - 1) = 0

Now we have a product of two expressions that is equal to zero, which means any x value that makes either (x - 8) or (x - 1) zero will make their product zero.

x - 8 = 0 => x = 8

x - 1 = 0 => x = 1

Therefore, our solutions are x = 8 and x = 1.