What value of 𝑥 solves the equation 𝑥 minus five over four minus one equals 𝑥 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 it’ll be easier to work with in this problem if it’s written as four over four.
Bring down the 𝑥 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 𝑥 minus five minus four over four is equal to 𝑥 over two.
For our next operation, we can subtract negative four from negative five, which would give us 𝑥 minus nine for our numerator. Our denominator hasn’t changed; it stays four.
Bring down the equals 𝑥 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 we’re left with 𝑥 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 𝑥 equals two 𝑥.
From here, we still have an 𝑥 on either side of the equation, so we need to get both our 𝑥 values on the same side. If I subtract 𝑥 from the left and the right side of the equation, I now have negative nine equals 𝑥.
If you’re wondering what happened in this second to last step, we had two 𝑥 and we subtracted 𝑥. Both of these 𝑥 values have a degree of one; this makes them like terms. So when we’re subtracting like terms, we subtract their coefficients; all we had to say was two minus one, which gave us negative nine equals 𝑥, or if you prefer 𝑥 equals negative nine.