How do you solve #5-2/(x-6) = (10-2x)/(x-6)#?

Question

Hazel Anglin · Accepted Answer

no solution

Let's give everything the same denominator. Fortunately, two of the three components already share the same denominator #(x-6)#. If we multiply #5# by #(x-6)/(x-6)#, all the components will be "combinable": #(5x-30)/(x-6) - 2/(x-6) = (10-2x)/(x-6)# Mix similar terms together #((5x-30)-(2))/(x-6) = (10-2x)/(x-6)# Multiply by (#x-6#) on both sides #5x-30-2 = 10-2x# Simplify #5x-32=10-2x# To both sides, add two times. #7x-32=10# Add #32# to both sides #7x=42# Divide by #7# on both sides #x=6# Just to check our work, let's solve the equation, replacing #x# with #6#: #5- 2/(6-6) = (10-2xx6)/(6-6)# #5-2/0=(-2)/0# Oh no! We're splitting by zero! There are no answers because that's against the law.

Isaiah Anthony · Answer

undefined To solve the equation 5-2/(x-6) = (10-2x)/(x-6), we can start by multiplying both sides of the equation by (x-6) to eliminate the denominators. This gives us 5(x-6) - 2 = 10 - 2x. Simplifying this equation, we get 5x - 30 - 2 = 10 - 2x. Combining like terms, we have 5x - 32 = 10 - 2x. Next, we can add 2x to both sides and add 32 to both sides to isolate the variable. This gives us 5x + 2x = 10 + 32. Simplifying further, we get 7x = 42. Finally, we can divide both sides of the equation by 7 to solve for x. This gives us x = 6. Therefore, the solution to the equation is x = 6.