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

Answer 1

Eli Assouline

First, distribute.

#(x - 3)/2 + 3/(2 - x) = 5x#

The LCD (least common denominator) is #(2)(2 - x)#

#((x - 3)(2 - x))/((2)(2 - x)) + ((3)(2))/((2 - x)(2)) = ((5x)(2)(2 - x))/((2)(2 - x))#

Now that everything is equal, you can remove the denominators.

#-x^2 - 3x + 2x - 6 + 6 = 20x - 10x^2#

#-x^2 - 21x + 10x^2 = 0#

#9x^2 - 21x = 0#

#3x(3x - 7) = 0#

#x = 0 and 7/3#

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Answer 2

Genesis Allen

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.