Solving any equation involves plotting a strategy to isolate the variable on one side of the equal sign. For these equations, you can "undo" what has been "done" to the variable. 1. 6(x-3) = 18 My guess is that you call this a "stage 2 equation" because it takes two steps to solve it. You solved equations like this when you first learned to multiply. You had, for example, one that looked like 6*___ = 18 Now, you know immediately that the blank ___ must be filled with 3 to make 6*3 = 18. This just means that the value of the stuff in brackets, that is (x - 3), is 3. Compare 6*___ = 18 to 6*(x-3) = 18 Thus, the problem reduces to (x - 3) = 3 You had problems like this when you first learned to add. ___ - 3 = 3 Now, you know immediately that ___ must be filled with 6 . This is the value of x. Here is an explanation in somewhat more formal terms. In the first example, we have subtracted 3 from the variable x and then multiplied the result by 6. To solve the equation, you divide the equation by 6, then add 3 to the result. 6(x - 3) = 18 (your original equation) (6(x - 3))/6 = 18/6 (divide the left side by 6, and divide the right side by 6) (x - 3)*(6/6) = 18/6 (rearrange the left side so we can see how to "cancel" the 6s) (x - 3)*1 = 18/6 (recognize that 6/6 = 1) x - 3 = 18/6 (recognize that anything times 1 is that thing) x - 3 = 3 (compute 18/6 = 3. Thus ends the first step of dividing the equation by 6. You will quickly learn to get to this point without the intermediate stuff.) (x - 3) + 3 = (3) + 3 (add 3 to both sides of the equation) x + (-3 + 3) = 3 + 3 (regroup so we can "cancel" the 3s) x + 0 = 3 + 3 (recognize that adding a number to its opposite gives 0) x = 3 + 3 (recognize that anything plus 0 is that thing) x = 6 (compute 3+3 = 6. Thus ends the second step of adding 3 to the equation. Here is our answer.) 2. 3(x+4)=15 Divide by 3 (x + 4) = 5 (the multiplier of 3 disappears from the left, and the right is a factor of 3 smaller.) Subtract 4 x = 1 (same as fill in the blank of ___ + 4 = 5) 3. 4(x+2)=16 Divide by 4 (x + 2) = 4 Subtract 2 x = 2 (same as fill in the blank of ___ + 2 = 4)
