What’s the answer

Question

When 7 times a number is decreased by 23, the result is the number plus 7. What’s the number

Answer 1

First step is to write an equation from the English sentence. This really is just translating the English into mathematics. Using "n" for "a number" this one would look as follows:

When 7 times a number [7n] is decreased by 23 [-23] the result is [that phrase means " = "] the number plus 7 [n + 7]

Putting the equation all together, you have:

7n -23 = n + 7

Now that you have an equation, solve it, step by step.

First subtract n from both sides, so that all the variables are on one side.

7n -23 = n + 7

-n -n

6n -23 = + 7

Next add + 23 to both sides so that the variable is all alone on the left side with no constants.

6n -23 = + 7

__+ 23 +23

6n = + 30

Now divide both sides of the equation by the coefficient of the variable which is +6

6n = + 30

6 6

n = 5

Now check it by putting 5 back into the equation

7n -23 = n + 7

7 (5) -23 = (5) + 7

35 -23 = 12

12 = 12

Answer 2

hello Dee:

Here, look at the wording.

When it says to decrease it means to Subtract, other wordings could be:

"FROM", "TAKE-AWAY", "REDUCED", REDUCED-BY".

So, we have:

7n - 23 = n+7

-n +23 =-n +23

________________

6n = 30

____ ___

6 6

n = 5

Check: 7(5) -23 = 5 +7

35 -23 =12

12 = 12

Hope this helps.