Question Video: Solving Linear Equations | Nagwa Question Video: Solving Linear Equations | Nagwa

# Question Video: Solving Linear Equations Mathematics • First Year of Preparatory School

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What value of ๐ฅ solves the equation ((๐ฅ โ 5)/4) โ 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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