### Video Transcript

What value of π₯ solves the equation π₯ minus five over four minus one equals π₯ 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 itβll be easier to work with in this problem if itβs written as four over four.

Bring down the π₯ 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 π₯ minus five minus four over four is equal to π₯ over two.

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

Bring down the equals π₯ 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 weβre left with π₯ 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 π₯ equals two π₯.

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

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