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What value of π₯ solves the equation π₯ minus five over four minus one equals π₯ over two?
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The first thing I wanna do is take this one and rewrite it as a fraction out of four.
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I wanna turn it into this: four over four.
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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.
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Bring down the π₯ minus five over four.
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And now our two fractions on the left side of the equal sign have a common denominator, which means we can subtract them.
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We can say π₯ minus five minus four over four is equal to π₯ over two.
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For our next operation, we can subtract negative four from negative five, which would give us π₯ minus nine for our numerator.
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Our denominator hasnβt changed; it stays four.
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Bring down the equals π₯ over two.
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To get rid of this four in the denominator, I can multiply both sides of the equation by four.
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On the left side, four divided by four equals one, so the fours cancel each other out, and weβre left with π₯ minus nine.
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On the right side, we have four over two, four divided by two.
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This can be simplified to two over one.
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Two times π₯ equals two π₯.
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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.
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If I subtract π₯ from the left and the right side of the equation, I now have negative nine equals π₯.
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If youβre wondering what happened in this second to last step, we had two π₯ and we subtracted π₯.
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Both of these π₯ values have a degree of one; this makes them like terms.
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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.