Most people are fairly comfortable with solving an equation such as<\/p>\n
2x -11 = 7x + 19<\/p>\n
By adding and subtracting quantities to both sides, you “get all the x terms to one side, and get all the numbers to the other side.”<\/p>\n
First, we might add 11 to both sides in order to get rid of the -11:<\/p>\n
2x = 7x + 30<\/p>\n
We might next subtract 7x from both sides in order to get rid of the 7x:<\/p>\n
-5x=30<\/p>\n
Finally, we divide both sides by -5:<\/p>\n
x=-6<\/p>\n
With a new question, let’s “take it to the next level”:<\/p>\n
3x\/5 +1 = x – 3\/2<\/p>\n
The fractions’ presence makes this question higher level than the last, since a new technique is needed. Specifically, we must clear out the fractions, by the following steps:<\/p>\n
Step 1<\/em><\/p>\n Identify the smallest number that both 5 and 2 divide into. The answer is 10.<\/p>\n Step 2<\/em><\/p>\n Multiply each term on both sides by the answer from Step 1 (10, in our case):<\/p>\n 10(3x\/5) +10(1) = 10x – 10(3\/2)<\/p>\n Step 3<\/em><\/p>\n Cancel where possible. For instance,<\/p>\n 10(3x\/5)=30x\/5=6x<\/p>\n On the non-fraction terms, there is no cancellation; we just mulitply them by 10.<\/p>\n The results of mulitplying each term by 10:<\/p>\n 6x + 10 = 10x – 15<\/p>\n We are back to the more familiar situation. From here, we might subtract 10 from both sides<\/p>\n 6x = 10x -25<\/p>\n Next, we’ll subtract 10x from both sides<\/p>\n -4x=-25<\/p>\n Finally, we’ll divide both sides by -4:<\/p>\n x=-25\/-4=25\/4<\/p>\n Answers can be – and often are – fractions.<\/p>\n I’ll be discussing algebra further in coming posts:)<\/p>\n