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.

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)