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Video: Solving Linear Equations with Real Numbers

Kathryn Kingham

Find the value of 𝑥 for which 5𝑥 + 4 = −5.

01:48

Video Transcript

Find the value of 𝑥 for which five 𝑥 plus four equals negative five.

Here we’re going to be solving a two-step equation. We can think of our goal here to isolate 𝑥. We want 𝑥 to be by itself on one side of the equal sign and everything else on the other.

In order to do that, we need to subtract four from both sides of our equation. Four minus four equals zero. Negative five minus four equals negative nine. We bring down the rest of our equation. Five 𝑥 plus zero equals five 𝑥.

I need to get rid of the five that’s being multiplied by 𝑥. We multiply five by its reciprocal because one-fifth times five equals one. But if we multiply one side of the equation by one-fifth, we have to multiply the other side of the equation by one-fifth so that they remain equal.

Like we’ve already said, one-fifth times five equals one. So on the left, we have one 𝑥 and on the right we’ve multiplied negative nine by one-fifth, which equals negative nine-fifths. One 𝑥 equals negative nine-fifths is another way of saying 𝑥 equals negative nine-fifths.