Question

Part 1

Solve 1/2 + 1/2x = x^2 − 7x+10/4x by rewriting the equation as a proportion. Which proportion is equivalent to the original equation?


Answer is C) x+1/2x = x^2-7x+10/4x


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Part 2


Name the true solution(s) to the equation

Answer: x = 1 and x = 8


Name the extraneous solution(s) to the equation.

Answer: x = 0

Answer 1

Part A: i forgot the question but i know its the third option (c)

Part B:

Solve the original equation by solving the proportion.

The solutions are: (1,6)

Part c:

Name the extraneous solution(s) to the equation

answer: Neither

These are for edu2020

Answer 2

Part 1.
`(x+1)/(2x)=(x^2-7x+10)/(4x).`

Part 2. Solutions:
`x_1=1,\ x_2=8.`

Extraneous solution:
`x=0.`

Explanation:

Part 1. You are given the equation

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

Note that

`(1)/(2)+(1)/(2x)=(x+1)/(2x),`

then the equation rewritten as proportion is

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

Part 2. Solve this equation using the main property of proportion:

`4x\cdot (x+1)=2x\cdot (x^2-7x+10),\\ \\2x(2x+2-x^2+7x-10)=0,\\ \\2x(-x^2+9x-8)=0.`

x cannot be equal 0 (it is placed in the denominator of the initial equation and denominator cannot be 0), so
`x=0` is extraneous solution to the equation.

Thus,

`-x^2+9x-8=0,\\ \\x^2-9x+8=0,\\ \\x_(1,2)=(9\pm√((-9)^2-4\cdot 8))/(2)=(9\pm7)/(2)=1,\ 8.`