How do you solve #1/2(x-3)+3/(2-x)=5 x#?

Answer 1

Abigail Allen

The soln. set is #{0,5/3}.#

#1/2*(x-3)+3/(2-x)=5x.#

#:. {(x-3)(2-x)+3*2}/(2(2-x))=5x.#

#:. (x-3)(2-x)+6=10x(2-x).#

#:. (x-3)(2-x)-10x(2-x)+6=0.#

#:. (2-x){x-3-10x}+6=0.#

#:.(2-x)(-9x-3)+6=0.#

#:.(x-2)(9x+3)+6=0.#

#:. 9x^2-18x+3x-6+6=0.#

#:. 9x^2-15x=0.#

#:. 3x(3x-5)=0.#

#:. x=0, or, x=5/3.#

As a result, it is simple to confirm that these roots fulfill the provided equation.

The soln. set is #{0,5/3}.#

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Answer 2

Savannah Anderson

To solve the equation 1/2(x-3)+3/(2-x)=5x, we can follow these steps:

Multiply through by the least common denominator, which is 2(x-3)(2-x). This will help eliminate the fractions.
Simplify the equation by distributing and combining like terms.
Rearrange the equation to isolate the variable x.
Solve for x by applying algebraic operations.

The final solution will be the value(s) of x that satisfy the equation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.