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How do I subtract 1/2x?

I have a question on the math lesson on “how to solve algebra problems” It’s lesson 2 practice questions with video answers. problem 5 which is 1/2x+5=4x-10

It made complete sense when you explained it in the video, which i am usually pretty good at algebra, but of course need to brush up 🙂

I’m curious as to why you can not use the reciprocal of 1/2x to both sides? this was my initial way to solve, but it of course did not give me the right answer. I did plug and chug and got the right answer but I feel like doing that every time will waste my time on the test.

Great question! Generally speaking, you can use the reciprocal once you get x isolated on one side of the equation. For example, with this equation…
1/2x + 5 = 4x -10
X is on both sides of the equal sign. This means I need to keep adding or subtracting. At this stage, I cannot use the reciprocal because x is on both sides of the equation.

For these types of algebra questions, you can only use the reciprocal after all the numbers are on one side and all the variables with coefficients are on the other. The steps are…

Step #1: Add and subtract, as needed to move variables to one side of the equation and numbers without variables to the other. In other words, add and subtract until the variable is isolated.

Step #2: Then, and only then, can you divide or multiply by the reciprocal.

In this case, it’s easier for me to divide by 3.5 rather than find the reciprocal of 3.5. 3.5 needs to be converted into a fraction, which is 7/2, so the reciprocal is 2/7.

15 x 2/7 does give you the answer, so the reciprocal is a valid method… but it can only be done once the variable is on only one side of the equation.

Finally, plug and chug is a perfectly valid way of finding the answer. You are right that it is time consuming, but keep it in your back pocket for emergencies. 🙂 One option to try is to plug and chug in order to check your work.

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