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Video: Solving One-Variable Equations

Bethani Gasparine

Solve the equation −6𝑥 − 1 = −23.

01:32

Video Transcript

Solve the equation negative six 𝑥 minus one equals negative 23.

In order to solve this equation, we need to solve for 𝑥. Therefore, our first step to isolate 𝑥 will be to get rid of the negative one and the opposite of subtracting one is adding one. And whatever we do to one side, we must do to the other. So negative one plus one is zero, which means they cancel, and then we’re left with a negative six 𝑥 on the left-hand side of the equation. And then, negative 23 plus one is negative 22.

Now, there’s only one step left to solve for 𝑥, to isolate it. We need to get rid of the negative six and the negative six is being multiplied to 𝑥. And the opposite of multiplying to 𝑥 would be to divide. So we divide both sides of the equation by negative six. Negative six divided by negative six is a positive one. But one 𝑥 is the same as 𝑥. So we can just write 𝑥.

And then on the right-hand side of the equation, negative 22 divided by negative six. Two negatives when dividing become a positive and 22 sixths can reduce. There is a number that goes into 22 and six. The largest number that goes into both would be two. 22 divided by two is 11 and six divided by two is three. So this means it reduces to 11 thirds. Solving our equation for 𝑥, we get that 𝑥 is equal to 11 thirds.