Question

The sum of three times a number n and 8 is no more than 25

Answer 1

Answer:
`(17)/(3)`

`\quad \begin{bmatrix}\mathrm{Solution:}\:&\:n<(17)/(3)\:\\ \:\mathrm{Decimal:}&\:n<5.66666\dots \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:(17)/(3)\right)\end{bmatrix}`

Explanation:

The question is an Algebra type of question. Before I learned Algebra, I usually just did as the question asked, I thought about what it meant. However, we can easily find the number "n" by following it in Algebraic terms.

Step 1: Set up an equation

• Pick out the values

"the sum of three times a number n and 8 is no more than 25"

Three times a number, "n"

`3n`

The sum means addition, so;

`3n\:+`

And 8. Combine;

`3n+8`

No more than 25, which means that both of them combined would still not result in something greater than 25, so it is less than 25.

`3n+8<25`

The Equation to solving the problem is
`3n+8<25`. Now we just have to solve it.

Step 2: Solve the equation

• Subtract 8 from both sides

`3n+8<25\\:\:\:\:\:-8\:\:\:-8`

Plus 8 minus 8 cancels out. So we are left with 25-8 = 17.

`3n<17`

• Divide both sides by 3

`(3n)/(3)<(17)/(3)\\\\n<(17)/(3)`

Answer 2

n = 17/3

or

(infinity, 17/3]

Explanation:

3n + 8 < 25

-8 < -8

3n < 17

3n/3 < 17/3

No more than would actually be less than or equal to. because the sum has to be under 25.