Final answer:
The equation '7 times some number added to 7 equals 19 added to the product of 4 and the number' can be solved by deductive algebraic manipulation, resulting in the number being sought as 4.
Step-by-step explanation:
The student is asking to solve the equation 7 times some number added to 7 equals 19 added to the product of 4 and the number. To represent the unknown number, we use a variable, such as 'x'. The equation can be written as 7x + 7 = 19 + 4x.
Let's solve the equation step-by-step:
- Subtract 4x from both sides to have all x terms on one side: 7x - 4x + 7 = 19 which simplifies to 3x + 7 = 19.
- Subtract 7 from both sides to isolate the term with x: 3x + 7 - 7 = 19 - 7 simplifying to 3x = 12.
- Divide both sides by 3 to solve for x: 3x / 3 = 12 / 3 resulting in x = 4.
The unknown number the student is seeking is 4.