### Video Transcript

What value of 𝑥 solves 𝑥 plus one over
two minus 𝑥 minus one over three is equal to 𝑥?

In order to solve this equation, we
firstly need to consider the left-hand side. In order to add or subtract any
fractions, we firstly need to make sure the denominators are the same. We do this by finding the lowest common
multiple or LCM. In this case, this would be six. We need to multiply the numerator and
denominator of the first fraction by three and the second fraction by two. The first fraction becomes three
multiplied by 𝑥 plus one over six. The second fraction, which has been
subtracted, becomes two multiplied by 𝑥 minus one over six. This is all equal to 𝑥. As the denominators are now the same, we
can write the left-hand side as a single fraction.

Our next step is to distribute the
parentheses, otherwise known as expanding the brackets. Three multiplied by 𝑥 is three 𝑥. And three multiplied by one is three. Negative two multiplied by 𝑥 is negative
two 𝑥. And negative two multiplied by negative
one is positive two. Remember, when we multiply a negative by
a negative, our answer is positive. The equation simplifies to three 𝑥 plus
three minus two 𝑥 plus two over six is equal to 𝑥. We can now simplify the numerator by
collecting or grouping like terms. Three 𝑥 minus two 𝑥 is equal to 𝑥, and
three plus two is equal to five. We have 𝑥 plus five over six is equal to
𝑥.

We can now solve this equation using the
balancing method and our knowledge of inverse operations. We begin by multiplying both sides by
six. This gives us 𝑥 plus five is equal to
six 𝑥. As there is a higher coefficient of 𝑥 on
the right-hand side, we can subtract 𝑥 from both sides. This gives us five is equal to five
𝑥. Finally, we divide both sides of this
equation by five. The value that solves the equation is 𝑥
equals one. We could check this by substituting this
value back in to the original equation.