Question:

Translate the mathematical phrase into symbol of "the difference between five times a number and eight is equal to the sum of thrice a number and two" then solve the problem.

Solution:

Let n be the number. Then translate the mathematical equation.

The Mathematical phrase "the difference between five times a number and eight is equal to the sum of thrice a number and two" translated to an algebraic equation is 5n - 8 = 3n + 2. The "n" represents the number, the "difference" means that you have to subract eight from five times a number, the "sum" means that you have to add two from thrice times a number and the "is equal to" that it means sign of equal.

Finding The Unknown Number In An Algebraic Equation.

Going back to the algebraic equation above, 5n - 8 = 3n + 2, let us now find the unknown number.

Solve for the unknown number.

• 5n - 8 = 3n + 2
• 5n - 3n = 2 + 8
• 2n = 10/2
• n = 5

The number is 5

Checking:

Plug in the number in the algebraic equation to check if the answer is correct.

If n = 5, then

• 5n - 8 = 3n + 2
• 5(5) - 8 = 3(5) + 2
• 25 - 8 = 15 + 2
• 17 = 17 ✔

Answer:

• Therefore, the number is 5