Video: Solving Linear Equations

What value of ๐‘ฅ solves the equation ((๐‘ฅ โˆ’ 5)/4) โˆ’ 1 = ๐‘ฅ/2?

02:55

Video Transcript

What value of ๐‘ฅ solves the equation ๐‘ฅ minus five over four minus one equals ๐‘ฅ 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 itโ€™ll be easier to work with in this problem if itโ€™s written as four over four.

Bring down the ๐‘ฅ 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 ๐‘ฅ minus five minus four over four is equal to ๐‘ฅ over two.

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

Bring down the equals ๐‘ฅ 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 weโ€™re left with ๐‘ฅ 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 ๐‘ฅ equals two ๐‘ฅ.

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

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

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