1. Equation Project All the steps on how to find ‘X’ Simplification Simplification Eliminating Variables Eliminating Variables Adding/Subtracting Constants Adding/Subtracting Constants Dividing by the Coefficient Dividing by the Coefficient All the steps on how to find ‘X’ Simplification Simplification Eliminating Variables Eliminating Variables Adding/Subtracting Constants Adding/Subtracting Constants Dividing by the Coefficient Dividing by the Coefficient *I apologize for the really bad drawings/line art and for the fact the style constantly changes ; - ;

2. Simplification If necessary, the first thing you do, is, of course, use the distributive property. The distributive property helps get rid of parentheses, and is how you multiply in algebra. All you need to do is multiply 2 5x to get 10x, and subtract 2 (which you get from ‘2 1’). 2(5x - 1) + 7 = 10 + x + 13 10x + 5 = 23 + x 2(5x - 1) + 7 = 10 + x + 13 10x + 5 = 23 + x Then you can Combine like terms. Basically it’s the process of simplifying an expression with addition and subtraction for the coefficients and ‘terms’. Like shown below, you can combine the like terms: 10 + 13 Because you add them, you can see that the expression above is equivalent to 23, the same applies to -2 + 7. dis·trib·u·tive (d-strby-tv) adj. 1.a. Of, relating to, or involving distribution. b. Serving to distribute. 2. Mathematics Of or relating to a rule that the same product results in multiplication when performed on a set of numbers as when performed on members of the set individually. If a × (b + c) = a × b + a × c, then × is distributive over +.

3. Eliminating Variables 2(5x - 1) + 7 = 10 + x + 13 10x + 5 = 23 + x -x 9x + 5 = 23 2(5x - 1) + 7 = 10 + x + 13 10x + 5 = 23 + x -x 9x + 5 = 23 The second step is eliminating variables. This is done to simplify further, by subtracting the most variables from both sides possible. 1 variable, or in this case, x, would be the amount subtracted. Subtracting (eliminating) x (the variable) from 10x + 5 equals 9x + 5. You then have to subtract x from the other side in order to even it out. Because this side only has one x, subtracting it leaves you with only 23. var·i·a·ble (vâr--bl, vr-) adj. 1.a. Likely to change or vary; subject to variation; changeable. b. Inconstant; fickle. 2. Biology Tending to deviate, as from a normal or recognized type; aberrant. 3. Mathematics Having no fixed quantitative value

4. Adding/Subtracting Constants 2(5x - 1) + 7 = 10 + x + 13 10x + 5 = 23 + x -x -x 9x + 5 = 23 -5 -5 9x 18 2(5x - 1) + 7 = 10 + x + 13 10x + 5 = 23 + x -x -x 9x + 5 = 23 -5 -5 9x 18 For the next step, we will have to subtract a constant. The most we can go is 5 (as shown in ‘9x + 5’), and since it is shown as plus five in the equation, it must be subtracted, from both sides con·stant (knstnt)n. 1. Something that is unchanging or invariable. 2. a. A quantity assumed to have a fixed value in a specified mathematical context. b. An experimental or theoretical condition, factor, or quantity that does not vary or that is regarded as invariant in specified circumstances. After subtracting 5 from 9x + 5, you will get the result of 9x. As for 23 – 5, 18 is the appropriate result. Now we know that 9x is equal to 18, and now. all we have to do to solve for x is divide

5. Division 2(5x - 1) + 7 = 10 + x + 13 10x + 5 = 23 + x -x -x 9x + 5 = 23 -5 -5 9x 18 9 9 X = 2 2(5x - 1) + 7 = 10 + x + 13 10x + 5 = 23 + x -x -x 9x + 5 = 23 -5 -5 9x 18 9 9 X = 2 And finally, the last step is to divide both sides by a coefficient, which in this case would be 9 (because of the ‘9x’). Dividing 9x by 9 equals, of course, x. So since 18 divided by 9 is 2, this means that x must equal 2. coefficient [ˌkəʊɪˈfɪʃənt] n 1. (Mathematics) Maths a. a numerical or constant factor in an algebraic term the coefficient of the term 3xyz is 3 b. the product of all the factors of a term excluding one or more specified variables the coefficient of x in 3axyz is 3ayz Even though this is the last step, to ensure the problem was done correctly, it’s always a good idea to check it so you know you won’t get it wrong.

6. Check Even if you think you got it right, it’s always a good idea to check your work. To do this you simply replace all variable with what it happens to equal, like so. Because the answers both had equivalent results, this proves the equation was completed correctly. This means that, for sure, X was 2, and now It’s done.