Problem 20 - Elementary Algebra

Question

Translate the phrases or sentences into mathematical expressions or equations for the following problems. A number is added to itself and this result is multiplied by the original number cubed. The result is twelve.

Step-by-Step Solution

Answer

Answer: The equation representing the problem is 2x^4 = 12.

Step 1: Understand the given information

An unknown number is added to itself, and the resulting sum is multiplied by that same unknown number raised to the power of three (cubed). The final result is twelve.

Step 2: Define the unknown number as a variable

Let x represent the unknown number.

Step 3: Translate the first part of the problem into an expression

Identify the operation of adding the unknown number to itself. This can be written as x + x or 2x (since it's the same number added twice).

Step 4: Translate the second part of the problem into an expression

Now, we need to multiply the sum from Step 3 by the original number cubed. The original number is x, so its cube is x^3. Multiplying the sum by the cube gives the expression 2x * x^3.

Step 5: Simplify the expression

Simplify the expression from Step 4 by multiplying 2x and x^3. Using the rules of exponents and multiplication, this simplifies to 2x^4.

Step 6: Formulate the equation

According to the problem, the result of the expression in Step 5 is twelve. So, set the simplified expression equal to twelve: 2x^4 = 12. Now the word problem has been translated into the equation 2x^4 = 12.