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

Answer 1

#x=0,15/9#

#(x-3)/2+3/(2-x)=5x#
Achieve a common denominator of #2(2-x)#.
#(x-3)/2((2-x)/(2-x))+(3/(2-x))(2/2)=5x#
#((-x^2+2x+3x-6)+6)/(4-2x)=5x#
#-x^2+5x=5x(4-2x)#
#-x^2+5x=-10x^2+20x#
#9x^2-15x=0#
#x(9x-15)=0#
#{(x=0),(9x-15=0rarrx=15/9):}#
Check to make sure that neither answer will cause a denominator to be #0#.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

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

  1. Multiply every term in the equation by the common denominator, which is 2(x-3)(2-x). This will help eliminate the fractions.

  2. Simplify the equation by distributing and combining like terms.

  3. Rearrange the equation to isolate the variable, x.

  4. Solve for x by dividing both sides of the equation by the coefficient of x.

  5. Check the solution by substituting the value of x back into the original equation to ensure it satisfies the equation.

The detailed steps are as follows:

  1. Multiply every term by the common denominator, 2(x-3)(2-x):

    (2(x-3)(2-x))(1/2(x-3)) + (2(x-3)(2-x))(3/(2-x)) = (2(x-3)(2-x))(5x)

  2. Simplify the equation by distributing and combining like terms:

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

  3. Expand and simplify further:

    (2-x) + 3x - 9 = 10x(x-3)(2-x)

  4. Rearrange the equation to isolate the variable, x:

    2 - x + 3x - 9 = 10x(x-3)(2-x)

    2x - 7 = 10x(x-3)(2-x)

  5. Solve for x by dividing both sides of the equation by the coefficient of x:

    2x - 7 = 10x(x-3)(2-x)

    2x - 7 = 10x(6 - 3x)

    2x - 7 = 60x - 30x^2

    30x^2 - 58x + 7 = 0

    (15x - 1)(2x - 7) = 0

    x = 1/15 or x = 7/2

  6. Check the solution by substituting the value of x back into the original equation:

    For x = 1/15:

    1/2(1/15 - 3) + 3/(2 - 1/15) = 5(1/15)

    The left side equals the right side, so x = 1/15 is a valid solution.

    For x = 7/2:

    1/2(7/2 - 3) + 3/(2 - 7/2) = 5(7/2)

    The left side equals the right side, so x = 7/2 is also a valid solution.

Therefore, the solutions to the equation 1/2(x-3) + 3/(2-x) = 5x are x = 1/15 and x = 7/2.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7