WEBVTT
00:00:01.340 --> 00:00:08.960
What value of π₯ solves the equation π₯ minus five over four minus one equals π₯ over two?
00:00:12.590 --> 00:00:18.410
The first thing I wanna do is take this one and rewrite it as a fraction out of four.
00:00:20.250 --> 00:00:23.200
I wanna turn it into this: four over four.
00:00:24.750 --> 00:00:32.960
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.
00:00:35.130 --> 00:00:37.640
Bring down the π₯ minus five over four.
00:00:38.840 --> 00:00:45.960
And now our two fractions on the left side of the equal sign have a common denominator, which means we can subtract them.
00:00:47.590 --> 00:00:55.350
We can say π₯ minus five minus four over four is equal to π₯ over two.
00:00:57.370 --> 00:01:06.870
For our next operation, we can subtract negative four from negative five, which would give us π₯ minus nine for our numerator.
00:01:08.270 --> 00:01:11.410
Our denominator hasnβt changed; it stays four.
00:01:12.600 --> 00:01:14.750
Bring down the equals π₯ over two.
00:01:16.790 --> 00:01:22.800
To get rid of this four in the denominator, I can multiply both sides of the equation by four.
00:01:25.830 --> 00:01:34.860
On the left side, four divided by four equals one, so the fours cancel each other out, and weβre left with π₯ minus nine.
00:01:36.600 --> 00:01:41.430
On the right side, we have four over two, four divided by two.
00:01:43.030 --> 00:01:46.460
This can be simplified to two over one.
00:01:48.020 --> 00:01:50.730
Two times π₯ equals two π₯.
00:01:52.680 --> 00:02:00.260
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.
00:02:02.240 --> 00:02:11.670
If I subtract π₯ from the left and the right side of the equation, I now have negative nine equals π₯.
00:02:13.280 --> 00:02:20.430
If youβre wondering what happened in this second to last step, we had two π₯ and we subtracted π₯.
00:02:22.620 --> 00:02:28.110
Both of these π₯ values have a degree of one; this makes them like terms.
00:02:28.380 --> 00:02:44.710
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.