Simplify the following expressions: 1. 3(2x-5) + 4(x+3) 2. If x−4=7, what is 2x+3? Provide the answer in the correct option.

The correct option is A.

The simplified expression is $\boxed{\text{A. } \textbf{10x - 3}}$.

Add 4 to both sides of the equation.

The correct option is not listed among A, B, C, D. Let me recheck my calculation.
$x-4=7 \implies x=11$.
$2x+3 = 2(11)+3 = 22+3 = 25$.
The options are A. 13, B. 17, C. 20, D. 27.
My calculated answer is 25, which is not among the options. There might be an error in the question's options. However, I must choose from the given options. I will state my calculated answer and note the discrepancy.

Given the strict instruction to choose from the options, and my calculation is 25, which is not an option, I cannot provide a correct option. I will state the correct numerical answer.

The value of $2x+3$ is $\boxed{\textbf{25}}$.
(Note: This answer is not among the provided options.)

The correct option is C.

The value of $x$ is $\boxed{\text{C. } \textbf{12}}$.

Distribute the negative sign to each term in $Q$.

Combine like terms.

The correct option is not listed among A, B, C, D. Let me recheck my calculation.
$P - Q = (2x^2 - 3x + 1) - (x^2 + 4x - 2) = 2x^2 - 3x + 1 - x^2 - 4x + 2 = x^2 - 7x + 3$.
Substitute $x=2$: $(2)^2 - 7(2) + 3 = 4 - 14 + 3 = -10 + 3 = -7$.
The options are A. 2, B. 4, C. 6, D. 8.
My calculated answer is -7, which is not among the options. There might be an error in the question's options. I will state the correct numerical answer.

The value of $P - Q$ when $x=2$ is $\boxed{\textbf{-7}}$.
(Note: This answer is not among the provided options.)

"A number $n$ is increased by 15" can be written as $n + 15$.
"the result is then multiplied by 3" means $3(n + 15)$.
"to give 60" means $3(n + 15) = 60$.

Divide both sides by 3.

Subtract 15 from both sides.

The correct option is B.

The value of $n$ is $\boxed{\text{B. } \textbf{5}}$.