Translate the phrase: "Seven more than twice a number is thirty-one" into an algebraic equation.

Which of the following pairs are consecutive even integers?

Solve: 4(x - 2) = 3x + 5. Which value of x satisfies the equation?

Solve the system where x + y = 50 and x = 2y - 5 by synthesizing the relations into one equation. Provide exact values for x and y.

Three consecutive integers are x, x+1, x+2. Determine if any integers satisfy the condition: twice the middle integer equals the sum of the other two integers plus 3. If a solution exists, find it; if not, explain why.