R/3=7 one-step equations: integers

  r = 21

Step-by-step explanation:

The "one step" is to undo the division by 3. To undo that division, you multiply both sides of the equation by 3. this gives you ...

  r·(3/3) = 7·3

  r = 21

The basic idea of any equation solution process is to "undo" what has been done to the variable. This is where the multiplication and addition identity elements come into play.

In this problem, the variable is multiplied by 1/3. The number that you multiply this by to get the identity element for multiplication (1) is the inverse of this fraction: 3/1, or 3. That is, 3 × 1/3 = 3/3 = 1. When 1 multiplies r, the result is just r, which is what you're trying to get to.

The rules of equality tell you that whatever you do to one side of an equation, you must also do to the other side. If you multiply r/3 by 3 on the left, then you must also multiply 7 by 3 on the right to keep the equation a true statement.

If the "one-step" involves addition ...

If the equation had been ...

  r + 3 = 7

Then the operation you need to "undo" is the addition of 3. That is accomplished by adding -3 to both sides of the equation. Then you have ...

  r + 3 - 3 = 7 - 3

  r + 0 = 4

  r = 4

You will recognize 0 as the additive identity element: r + 0 = r. In order to get that (0) as a sum, you need to add opposites: +3 -3 = 0. Again, you have to do the same thing (add -3) to both sides of the equation in order to keep it true.

11 feet 6 inches and 8 feet 6 inches

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