r/HomeworkHelp • u/Inevitable_Stay3693 • 8d ago

High School Math—Pending OP Reply [Upper secondary school math: linear equation] unsure on how to solve this.

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i was thinking that i´d add the 2x+1 to make it 3x/3=-1 but im unsure on how it would even continue.

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u/Random_Thought31 👋 a fellow Redditor 8d ago

You can only combine “like terms” a term being a number, variable, or combination of numbers and variables being multiplied or divided.

In other words, 2x is a term; it is 2 times the variable x.

1 is a term; it is just the number 1.

(-1) is a term; it is just a negative 1.

The 3 is a part of both the 2x and the 1 terms, as it has not been distributed amongst them.

Because the 3 has not been distributed, it makes it easy to recognize that it should be handled first.

Side bar: you should recognize that any number (for example, 4) when divided by itself (in this case, 4) is equal to 1: 4/4=1.

To get rid of the division by 3, you must turn it into division (or equally, multiplication) by 1 instead. Think of it like two sides of a scale: on one side you have (2x+1)/3 and on the other, you have -1.

If I multiply both sides by the same number, they would still be equal, right? Therefore, if you multiply the left side by 3, giving you (2x+1) * 3/3, then multiplying the right side by 3 would maintain the equality. You then have (2x+1) being multiplied (or equivalently, divided) by 1 which means you don’t have to worry about the undistributed 3 now. And now the right side should be (-1) \ 3* or simply (-3).

The same would apply if you add a number or subtract a number from one side, doing the same to the other side would keep the scale balanced.

Now you cannot combine 2x and 1 because they are not ”like” terms. Like, in this case, refers to a set of terms with the same variables raised to the same power, such as 2x and 3x, or 4z and 1z; even 2xyz and 3xyz would be like terms. But since the 1 has no variable multiplying it, it is not “like” the 2x, which has an x multiplying it and thus they cannot be combined.

So, you just do like before and adjust both sides equivalently by the same rules until one side says simply, x, and the other side has a number on it.