Solve the Fraction Equation: Finding X in 1/3x + 5/6 = -1/6

Question

Find the value of the parameter X

13x+56=16 \frac{1}{3}x+\frac{5}{6}=-\frac{1}{6}

Video Solution

Solution Steps

00:00 Solve the following expression
00:03 We want to isolate the unknown X
00:07 Arrange the equation with the unknown X on one side
00:19 Simplify
00:34 Multiply by the denominator in order to eliminate the fraction
00:44 Simplify further
00:50 Here is the solution

Step-by-Step Solution

First, we will arrange the equation so that we have variables on one side and numbers on the other side.

Therefore, we will move 56 \frac{5}{6} to the other side, and we will get

13x=1656 \frac{1}{3}x=-\frac{1}{6}-\frac{5}{6}

Note that the two fractions on the right side share the same denominator, so you can subtract them:

 13x=66 \frac{1}{3}x=-\frac{6}{6}

Observe the minus sign on the right side!

 

13x=1 \frac{1}{3}x=-1

 

Now, we will try to get rid of the denominator, we will do this by multiplying the entire exercise by the denominator (that is, all terms on both sides of the equation):

1x=3 1x=-3

 x=3 x=-3

Answer

-3