How do you solve #(5x)/2 - x = x/14 + 9/7#?

Question

Savannah Anderson · Accepted Answer

#x=9/10#

We have an equation which has fractions.

#(5x)/2 - x = x/14 + 9/7#

We can get rid of the fractions immediately by multiplying the whole equation by the LCM of the denominators, which is #14#

#(color(blue)(cancel14^7xx)5x)/cancel2 -color(blue)(14xx) x = (color(blue)(cancel14xx)x)/cancel14 + (color(blue)(cancel14^2xx)9)/cancel7" "larr# cancel

#" "35x -14x = x+18#

#35x-14x-x= 18#

#color(white)(xxxxxxxx)20x = 18#

#color(white)(xxxxxxxxx)x= 18/20#

#color(white)(xxxxxxxxx)x=9/10#

Abigail Allen · Answer

#x = 9/10#

#(5x)/2 - x = x/14 + 9/7#

Let's get a common denominator for the left side of the equation

#(5x)/2 - x xx 2/2 = x/14 + 9/7#

#(5x - 2x)/2 = x/14 + 9/7#

#(3x)/2 = x/14 + 9/7#

Let's get all the #x#s on the same side

#(3x)/2 - x/14 = 9/7#

Common denominator

#7/7 xx (3x)/2 - x/14 = 9/7#

#(21x)/14 - x/14 = 9/7#

Let's get another common denominator (we don't technically need this, but it makes the math easier later)

#(20x)/14 = 9/7 xx 2/2#

#(20x)/14 = 18/14#

Multiply both sides by #14#

#20x = 18#

Divide by #20# on both sides

#x = 18/20#

#x = 9/10#

Jameson Allen · Answer

undefined To solve the equation (5x)/2 - x = x/14 + 9/7, you can follow these steps:

1. Multiply every term in the equation by the least common denominator (LCD) of 14 to eliminate the fractions. This will result in:
   7(5x)/2 - 7x = x + 18/2

2. Simplify the equation:
   (35x)/2 - 7x = x + 9

3. Multiply every term in the equation by 2 to eliminate the fraction in the first term:
   35x - 14x = 2x + 18

4. Combine like terms:
   21x = 2x + 18

5. Subtract 2x from both sides of the equation:
   19x = 18

6. Divide both sides of the equation by 19 to solve for x:
   x = 18/19

Therefore, the solution to the equation (5x)/2 - x = x/14 + 9/7 is x = 18/19.