the product of 5 and the cube of x, increased by the difference of 6 and x3

Given the statement:

The product of 5 and the cube of x, increased by the difference of 6 and x^3.

It can be written as,

5x^3 + (6 - x^3)

Explanation:

The product means multiplication of two numbers, and cube means raising the number to a degree of 3, or having an exponent of 3. Now we've used the plus sign since it is stated that the number is increased by, which means that the operation involves addition.  For the difference, it mean subtraction, therefore we've used the minus sign.

Solution:

In order to solve for x, we combine similar terms.

5x^3 + (6 - x^3)

5x^3 + 6 - x^3

4x^3 + 6

Transpose 6 on the other side of the equation, note that when transposing a number, the sign changes.

4x^3 = -6

Divide both sides by 4, in order to cancel out 4x^3.

4x^3 /4= -6/4

x^3 = -6/4

Take the cube root of each side in order to determine the value of x, cube root can be represented as raising the number by ⅓.

(x^3)^⅓ = (-6/4)^⅓

x = -1.14

Final answer:

Numerical form = 5x^3 + (6 - x^3)

Value of x = -1.14