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

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

Step-by-step 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"

[tex]3n[/tex]

The sum means addition, so;

[tex]3n\:+[/tex]

And 8. Combine;

[tex]3n+8[/tex]

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.

[tex]3n+8<25[/tex]

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

Step 2: Solve the equation

Subtract 8 from both sides

[tex]3n+8<25\\:\:\:\:\:-8\:\:\:-8[/tex]

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

[tex]3n<17[/tex]

Divide both sides by 3

[tex]\frac{3n}{3}<\frac{17}{3}\\\\n<\frac{17}{3}[/tex]