nine times the difference of a number and 3 is the same as 3 increased by nine times the number plus three times the number

Question

i just wanna know the answer and to be shown in number form.

Answer 1

ELA context clues play an important role in these questions- if we know what the word means, we can translate the equation into numbers and symbols:

Context Clues

Times ~ Multiplication

Difference ~ The result of a subtraction problem

'a number' ~ We may not know what this number is, but we can name it something! Let's call it 'n' for 'number'

Is/same as ~ Both the words 'is' and 'same as' imply an equal (=) sign

Increased by/plus ~ 'increased by' and 'plus' both imply Addition

With all this information, and reading our question carefully, we can decipher the following:

9(n-3) = 3 + (9n + 3n)

Now that we see a question in numbers and symbols, I can work out that we clearly need to solve for n. We can solve for n, by isolating variable n. To do this, we figure out functions in the equation, like multiplication, division, addition and subtraction, and change how the equation looks by using Inverse functions:

Inverse Functions (Opposite functions)

Division (/) ==> Multiplication (*)

Multiplication (*) ==> Division (/)

Addition (+) ==> Subtraction (-)

Subtraction (-) ==> Addition (+)

Now to tackle the problem and solve for n:

9(n-3) = 3 + (9n + 3n)

9n - 27 = 3 + (9n +3n) (Step 1. Distributive Property)

9n - 27 = 3 + 12n (Step 2. Combine like terms; 9n + 3n = 12n)

-9n -9n (Step 3. Subtract 9n from both sides to isolate the variable)

______________

-27 = 3 + 3n

-3 -3 (Step 4. Subtract 3 from both sides)

________________

-30 = 3n

----- ----

3 3 (Step 5. Divide 3 from both sides)

________________

-10 = n

Therefore, n = -10

Please let me know if this answer was helpful!

Sincerely,

Derek D.