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Similarities Between Equations And Inequalities

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In Algebra, we have been learning about Equations and Inequalities, and how you can solve them in the same ways. Though, They’re both very similar and both very different in their own ways, which makes it difficult to find the differences.
But, There are also many similarities between them. The way that the two are similar is that you can solve both problems the same way, for example:
If you had 2x + 2 = 10
You’d solve it by subtracting 2 with 10, which would result in an 8.

2x + 2 = 10
2x = 8

After this, you’d divide 2 with 2, and 2 with 8, which would give you a 4.
So the answer would be X = 4. So 4 would be the only answer.

2x + 2 = 10
2x = 8
X = 4

If you did this with an IneQuality, it would turn out the same, except if you divide …show more content…

-2x + 2 < 10 ( Reversed equation )
2x < 8
Once you subtract two with the ten, you’d have to reverse the sign because the negative is with the ‘ x’, which would make the problem x is greater than 4.

X > 4.

With inequalities, this would be all numbers less than 4 instead of being only 4 as the answer.

But, A difference between the two would be graphing the answers. After we both get 4 for both of the problems, we’d need to graph both of the answers. But, in both you’re still trying to find the unknown number which is shown to be a variable, or simply put, ‘ x ‘ .

When it comes to the simple Equation that was done first, the graphing would look like this:

-------- 3 4 5

It would be a closed circle with no arrows, since that 4 is the only answer, and it can’t be greater than or less than, just equal to 4 itself.

But when it comes to the Inequality equation, the graphing is a bit …show more content…

Since its all numbers less than 4, we’d have an open circle since it isn’t equal to 4. And there's an arrow pointing towards the left since its all numbers less than 4.
But, if it was all numbers greater than 4, it would be like this: --
--------
3 4 5

Despite the two having a couple differences and a couple similarities, both can be used in the world around us, since, depending on the symbol you use, you’d still get the same answer nonetheless.

However, there still are more differences between the two.
Even if you do the Math equation the same, the symbols can cause the answer to shift, and make it so the two aren’t the same.

For example:

If you used 12x + 6 = 6 (2x+1 )
You’d start by multiplying the 6 by 2, since the 6 is next to a parenthesis symbol, which would give you 12, and you’d multiply the 6 with 1, which would give you 6 in return.

12x + 6 = 6 (2x+1)
12x + 6 = 12x+6

tHEN, YOU’D SUBTRACT 12 BY ITSELF, AND WITH THE OTHER 12, WHICH WOULD MAKE THE ANSWER 6 = 6, MAKING IT AN INFINITE SOLUTION.

12x + 6 = 6 (2x+1)
12x + 6 = 12x+6
6 = 6

bUT, IF YOU DID THIS WITH AN INEQUALITY, YOU’D GET A COMPLETELY DIFFERENT

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