r/HomeworkHelp • u/Inevitable_Stay3693 • Aug 27 '26
High School Math—Pending OP Reply [Upper secondary school math: linear equation] unsure on how to solve this.
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/BubbleRocket1 Aug 27 '26
You cannot add the numerator together because of the x. If it helps for visualization, have variable u = 2x+1.
Now the equation is u/3 = -1. I think the rest should be able to fall into place from here
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u/paperic Aug 27 '26
2x+1 to make it 3x/3=-1
That's not correct, as others said.
It's an equation, that means both sides are the same.
It also means if you do the same thing to both sides, they'll keep being the same.
Generally, what typically works is to do the opposite of what you see.
(2x+1) / 3 = -1.
The biggest pain point is the "divide by 3" on the left. So do the opposite of that. Multiply it by 3!
(multiply both sides, ofcourse, to keep them equal)
On the right side 3 * (-1) will turn into -3.
On the left side, the "3 *" will exactly undo the "/ 3", so you end up with
2x+1 = -3
Now it's easy.
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u/igotshadowbaned Aug 27 '26
(2x+1)/3 = -1
(2x+1)/3 • 3 = -1 • 3
2x+1 = -3
Continue
Upper secondary school math
And I'm afraid that's not an accurate descriptor of the level of math that this is
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u/Impossible_Dog_7262 Aug 27 '26
How is this upper secondary.
Multiply both by 3, subtract 1, divide by 2. x = -2
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u/zon5string Aug 27 '26
Multiply both sides by 3 to remove the denominator.....2x+1 = -3. I'll let you go from there.
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u/Ok_Objective_5192 Aug 27 '26
Fractions are hard to work with. As a first step, is there anything you can do to both sides of the equation that would get rid of the fraction?
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u/iufan417 Aug 27 '26
Fractions aren't hard to work with for the very reason you just hinted.
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u/Ok_Objective_5192 Aug 27 '26
Yeah I meant contextually given OP's question and thought process. That was meant as guidance, not a declarative statement on how workable fractions are
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u/Then-Dragonfruit6945 Aug 27 '26
The idea is to isolate the x by applying the same operation to both sides (so the equallity holds) First we multiply each side by 3 (you can see how the denominator cancels with the new 3 and "goes away") then we need to keep going until we only have the x on the LHS.
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u/Paper-Hero Aug 27 '26
Multiply both sides by three. Then bring the like terms together.. Finish the arithmetic to find x.
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u/Random_Thought31 Aug 27 '26
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.
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u/360alaska Aug 28 '26
Muiltiply both sides by 3 to clear the /3 , then you have 2x+1=-3, then subtract 1 from both sides, 2x= -4 , then divide by 2 = x =-2.
Start with dividing by 3 here, it is low hanging fruit.
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u/Angrybirds159 Aug 27 '26
2x + 1 isn't 3x. that's like saying 2 apples + one orange is 3 apples. 2x + 1x would be 3x
the way I'd solve it is
(2x+1)/3 = -1 we multiply by 3 in both sides (the three goes over, multiplying)
2x + 1 = -1 * 3
2x + 1 = -3 now we subtract one from both sides
2x = -3 -1
2x = -4 x = -2