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# One-step division equations

Let's ease into this, shall we? Here's an introduction to basic algebraic equations of the form ax=b. Remember that you can check to see if you have the right answer by substituting it for the variable! Created by Sal Khan.

## Want to join the conversation?

• At , when he multiplies by 1/3 what is his motivation to choose that specific number? (Fraction) Can you multiply by a different number, a whole number, for example?
• He chose 1/3 because he wanted to turn the coefficient (3) into a 1. The way you turn a 3 into a one is to divide by 3. You can do this with any number. Any number divided by itself is equal to 1. 4/4=1, 5/5=1, 287/287=1. Because any number multiplied by 1 is that number, he is left with (in the 3x=15 problem)when you divide both sides by 3, you change the 3 into a 1 and the 15 into a 5, leaving you with (1 times x = 15). Since one times anything is itself, we can forget about the 1 and we are left with x=15.
• @ , Sal uses the word Coefficient. What does that mean?
• Coefficient is just the proper name for the number in front of the x. It's the amount that x is multiplied by.

7x=14, here, the coefficient of x is 7
• Can i know from where did you get the 1/3?
• He got 1/3 because the left side was 3x. If, for example, he had 4x, he would have multiplied by 1/4; if he had 5x, he would have multiplied by 1/5, and so on.
• Why is "x" used in algebra to represent a variable?
• Apology for the late answer but I think it is worth your while!
The Arabic term al-jabr as what in English is now known as: “algebra”. Most of our mathematical words also come from Arabic. X, is no different. The word for the unknown in Arabic was Shay-un, however when Spanish translators began to translate the word, then encountered a problem: There is no 'sheen' (the first letter in Shay-un, making the sh sound) in Spanish. Thus they replaced it with the Greek letter Chi, making the sound Ch which is represented by, you guessed it: an X.
Hope this helps! ~Rhi
• At where did you get the 1/3 and how come 15 times 1/3 = 1x ?
• It's the same thing as dividing by 3.If you multiply the three by the 1/3, you get 3/3x, which simplifies to 1x. When you do that to the other side,you get 15/3, which simplifies to 5.
• What Does The Method For Mean ?
• If you have an equality, you can do the same operations to both sides of the equality and the resulting equality holds true. In this case
7x = 14
you divide by 7 on both sides
7x/7 = 14/2
and then simplify the left side (7/7=1) and calculate the right side (14/7=2)
x=2
• How would you do division problems with negative numbers when you are solving equations?
• Here are the Instructions for the Multiplication and Division of integer numbers. Hope it help:

III- MULTIPLICATION: Very easy if you remember these 3 rules

Rule No. 1: A positive number multiplied by a negative number always results in a negative number. Example: (+60) x (-3) = -180

Rule No. 2: A negative number multiplied by a negative number always results in a positive number. Example: (-15) x (-3) = +45 or 45 (without a sign, means positive)

Rule No. 3: A positive number multiplied by a positive number always results in a positive number. Example: (+30) x (+8) = +240 or 240 (without a sign, means positive)

IV- DIVISION: 3 rules, very similar to the 3 rules of Multiplication

Example 1: +48 ÷ -3 = -16
Example 2: +48 ÷ +3 = 16
Example 3: -48 ÷ -3 = 16
• how solving two step equation different from solving one step equation?
• Not at all different, just more steps required to isolate and solve for the variable.
One Step: x - 5 = 10
More than one step: (2/3)x - 5 = 6x + 1/2