### Video Transcript

What value of ๐ฅ solves the equation ๐ฅ minus five over four minus one equals ๐ฅ over two?

The first thing I wanna do is take this one and rewrite it as a fraction out of four. I wanna turn it into this: four over four. I know that four over four is still equal to one, but itโll be easier to work with in this problem if itโs written as four over four.

Bring down the ๐ฅ minus five over four. And now our two fractions on the left side of the equal sign have a common denominator, which means we can subtract them. We can say ๐ฅ minus five minus four over four is equal to ๐ฅ over two.

For our next operation, we can subtract negative four from negative five, which would give us ๐ฅ minus nine for our numerator. Our denominator hasnโt changed; it stays four.

Bring down the equals ๐ฅ over two. To get rid of this four in the denominator, I can multiply both sides of the equation by four. On the left side, four divided by four equals one, so the fours cancel each other out, and weโre left with ๐ฅ minus nine. On the right side, we have four over two, four divided by two. This can be simplified to two over one. Two times ๐ฅ equals two ๐ฅ.

From here, we still have an ๐ฅ on either side of the equation, so we need to get both our ๐ฅ values on the same side. If I subtract ๐ฅ from the left and the right side of the equation, I now have negative nine equals ๐ฅ.

If youโre wondering what happened in this second to last step, we had two ๐ฅ and we subtracted ๐ฅ. Both of these ๐ฅ values have a degree of one; this makes them like terms. So when weโre subtracting like terms, we subtract their coefficients; all we had to say was two minus one, which gave us negative nine equals ๐ฅ, or if you prefer ๐ฅ equals negative nine.