Final answer:
To solve the equation, set it up as 4x = x + 51 and solve for x.
Step-by-step explanation:
To find the number that satisfies the equation four times a number is equal to the number increased by fifty-one, we can set up an equation. Let's call the number 'x'. The equation is then 4x = x + 51. We can solve for x by subtracting x from both sides of the equation: 4x - x = 51. Simplifying, we have 3x = 51. Finally, we divide both sides by 3 to isolate x: x = 51 / 3. Evaluating the division, we find that x is equal to 17.