Question 1118514: It’s been awhile since I have had Algebra. I looking at an equation that I just don’t get! 10x + 2=7 How do I start looking at the formula for this! Thank you in advance
Found 5 solutions by math_helper, ikleyn, josgarithmetic, greenestamps, Shin123:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! 10x + 2 = 7 is an equation. There is no formula per-se, instead one might wish to figure out what x is. This is called "solving for x" ( x will typically represent an unknown quantity, and, when it is possible to reduce it to a known value, that's usually what we'd like to do. )
One thing about equations, whatever you do to one side you can do to the other side without affecting the equality:
For instance, subtracting 2 from both sides:
10x + 2 - 2 = 7 - 2
Leaves us with:
10x = 5
Now dividing both sides by 10:
10x/10 = 5/10
Notice that on the left hand side, we have 10x/10 and the tens cancel (or you can say 10/10 = 1) leaving just "one x" on the left, which is just written x by itself:
x = 5/10
We've solved for x.
Usually, we take one additional step to reduce the fraction to lowest terms (we can divide a fraction's numerator and denominator by a nonzero number without changing the fraction):
x = (5/5) / (10/5) = 1/2
Ans: 
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Check: 10(1/2) + 2 = 5 + 2 = 7 (ok)
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To the student: Thank you for the nice thank you note. Feel free to ask more questions. Also, as tutor @ikleyn says, she and others have posted a lot of lessons here to refresh/enlighten you. Best wishes.
Answer by ikleyn(52767)  (Show Source):
Answer by josgarithmetic(39615)  (Show Source):
You can put this solution on YOUR website! You need no formula. Just know the basic algebra rules.
How do you undo this and reveal x?
In this order:
(1) Additive Inverse Property
(2) Multiplicative Inverse Property
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Tutor @math_helper has given you a good step-by-step demonstration of a formal algebraic way to solve your problem.
Tutor @josgarithmetic has hinted at a method for solving the problem informally, using logical reasoning.
And if you do what he SUGGESTS that you do, you find that the formal algebra does EXACTLY the same thing as the informal solution.
Think about what the given equation says. It says you took a number, multiplied it by 10, then added 2, and ended up with a result of 7.
The informal method of solving the problem says that to get back where you started, you need to "undo" the things you did to the original number.
The last thing you did to get your final answer of 7 was add 2; to undo that, you need to subtract 2. 7-2 = 5.
In the formal algebraic solution, that looks like this (as shown in @math_helper's solution):
10x + 2 = 7 --> 10x + 2 - 2 = 7 - 2 --> 10x = 5
Continuing to work backwards, the first thing you did to the number you started with was multiply by 10. To undo that, you need to divide by 10. Informally, you simply say 5 divided by 10 is 5/10, or 1/2; so that is the number you started with.
In the formal algebraic solution, that step looks like this:
10x = 5 --> 10x/10 = 5/10 --> x = 5/10 = 1/2
Answer by Shin123(626)  (Show Source):
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