Let the unknown number be \(\displaystyle x\).

Three more than six times a number:  \(\displaystyle 6x+3\)

Two less than the same number:  \(\displaystyle x-2\)

The "and" would separate the quantities and the product would be:  

\(\displaystyle (6x+3)(x-2)\)

The answer is:  \(\displaystyle (6x+3)(x-2)\)

Solve this question by first writing the inner quantity of the cube root.

Two times a number squared:  \(\displaystyle 2x^2\)

The cube root of two times a number squared:  \(\displaystyle \sqrt[3]{2x^2}\)

The answer is:  \(\displaystyle \sqrt[3]{2x^2}\)

Split the statement into parts.

Three times a number:  \(\displaystyle 3x\)

The fifth root of three times a number:  \(\displaystyle \sqrt[5]{3x}\)

Five times the fifth root of three times a number:  \(\displaystyle 5\sqrt[5]{3x}\)

The answer is:  \(\displaystyle 5\sqrt[5]{3x}\)

An expression cannot contain an equal sign or inequality sign.

Start with the quantity.

Five times a number less than five:  \(\displaystyle 5-5x\)

Nine times the quantity of five times a number less than five:  \(\displaystyle 9(5-5x)\)

The answer is:  \(\displaystyle 9(5-5x)\)

Break up the sentence into parts.

The quantity of six less than twice a number:  \(\displaystyle 2x-6\)

The fifth root of the quantity of six less than twice a number:  \(\displaystyle \sqrt[5]{2x-6}\)

The answer is:  \(\displaystyle \sqrt[5]{2x-6}\)

Start by taking the difference of the two numbers.

The difference of twice a number and six:  \(\displaystyle 2x-6\)

The square of the difference of twice a number and six:  \(\displaystyle (2x-6)^2\)

Be careful not to mix the terms of square and square root.

The answer is:  \(\displaystyle (2x-6)^2\)

Start with the quantity.

Three less than five times a number:  \(\displaystyle 5x-3\)

This term is a quantity.

The fourth root of the quantity:  \(\displaystyle \sqrt[4]{5x-3}\)

The answer is:  \(\displaystyle \sqrt[4]{5x-3}\)

Break up the terms and write each part.

Twice a number:  \(\displaystyle 2x\)

Three times another number cubed:  \(\displaystyle 3y^3\)

Is eight:  \(\displaystyle =8\)

Sum the two different numbers that is equal to eight.

The answer is:  \(\displaystyle 2x+3y^3 = 8\)

Break up the sentence into parts.

Twice a number squared:  \(\displaystyle 2x^2\)

The fourth root of twice a number squared:  \(\displaystyle \sqrt[4]{2x^2}\)

Do not mix split this radical and pull out the coefficient!

The answer is:  \(\displaystyle \sqrt[4]{2x^2}\)

Split the sentence into parts.

The cube of a number:  \(\displaystyle x^3\)

Eight times the cube of a number:  \(\displaystyle 8x^3\)

Five less than eight times the cube of a number:  \(\displaystyle 8x^3-5\)

Is negative eleven:  \(\displaystyle =-11\)

The answer is:  \(\displaystyle 8x^3-5 =-11\)