When you tutor math, you see various approaches to algebra.\u00a0 Here’s my interpretation:<\/p>\n
1)\u00a0 Decide which side you want “x” (or whatever variable you have).<\/p>\n
2)\u00a0 Get all the x terms to that<\/em> side, and all the numbers to the other side.<\/p>\n To do this, you perform a series of operations:\u00a0 always the same\u00a0<\/em>to both sides.<\/p>\n 3)\u00a0 Divide out the coefficient of x.<\/p>\n Here’s an example:<\/p>\n 7x – 1 = 5x + 9<\/p>\n Let’s get the x’s on the left.\u00a0 To get rid of the 5x on the right, we subtract 5x from both sides:<\/p>\n 7x – 1 = 5x + 9<\/p>\n -5x\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0-5x<\/p>\n On the left, 7x – 5x = 2x.\u00a0 On the right, 5x – 5x = 0.\u00a0 We are left with:<\/p>\n 2x – 1 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a09<\/p>\n Now, let’s get the numbers to the other side.\u00a0 To get rid of a -1, we add 1 (as always, to both sides)<\/em>:<\/p>\n 2x\u00a0 –\u00a01 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a09<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0 +1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0+1<\/p>\n 2x\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10<\/p>\n Now we divide both sides by the coefficient of x, which is 2, to cancel it. Then we get the result:<\/p>\n x\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5<\/p>\n I’ll be talking more about\u00a0algebra, of course,\u00a0but\u00a0for the first day back, this is probably good.<\/p>\n