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Question Video: Solving Linear Equations Mathematics • 7th Grade

What value of π‘₯ solves the equation ((π‘₯ βˆ’ 5)/4) βˆ’ 1 = π‘₯/2?

02:55

Video Transcript

What value of π‘₯ solves the equation π‘₯ minus five over four minus one equals π‘₯ 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 π‘₯ 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 π‘₯ minus five minus four over four is equal to π‘₯ over two.

For our next operation, we can subtract negative four from negative five, which would give us π‘₯ minus nine for our numerator. Our denominator hasn’t changed; it stays four.

Bring down the equals π‘₯ 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 π‘₯ 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 π‘₯ equals two π‘₯.

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. If I subtract π‘₯ from the left and the right side of the equation, I now have negative nine equals π‘₯.

If you’re wondering what happened in this second to last step, we had two π‘₯ and we subtracted π‘₯. Both of these π‘₯ 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 π‘₯, or if you prefer π‘₯ equals negative nine.

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