Question

Fourteen more than three times a number is equal to the difference between −51

and twice the number. Find the number.

Answer 1

The student's algebra problem involves setting up and solving a linear equation. The equation, based on the problem statement, is 3x + 14 = -51 - 2x. Solving this equation, we find that the number in question is -13.

Step-by-step explanation:

The question presented is a typical linear equation problem, which requires finding the value of a number that satisfies a given condition. We are told that 'fourteen more than three times a number is equal to the difference between −51 and twice the number'. This can be translated into an algebraic equation which we can solve step-by-step.

Let's define the unknown number as x. Then, we can write the equation as:

3x + 14 = -51 - 2x

To find the value of x, we need to bring like terms together:

1. Add 2x to both sides of the equation to get all x terms on one side:
2. 3x + 2x + 14 = -51
3. 5x + 14 = -51
4. Subtract 14 from both sides to isolate the term with x:
5. 5x = -51 - 14
6. 5x = -65
7. Divide both sides by 5 to solve for x:
8. x = -65 / 5
9. x = -13

Therefore, the number we are looking for is x = -13.