Algebra II : Setting Up Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #111 : Equations

Set up the equation:  Three less than five times the square root of a number is fourteen.

Possible Answers:

\(\displaystyle 3-\sqrt{5x} =14\)

\(\displaystyle \sqrt{5x}-3 =14\)

\(\displaystyle \sqrt{5x-3} =14\)

\(\displaystyle 5\sqrt{x}-3 =14\)

\(\displaystyle 3-5\sqrt{x} =14\)

Correct answer:

\(\displaystyle 5\sqrt{x}-3 =14\)

Explanation:

Break up the sentence into parts.

The square root of a number: \(\displaystyle \sqrt{x}\)

Five times the square root of a number: \(\displaystyle 5\sqrt{x}\)

Three less than five times the square root of a number:  \(\displaystyle 5\sqrt{x}-3\)

Is fourteen:  \(\displaystyle =14\)

Combine the parts to form the equation.

The answer is:  \(\displaystyle 5\sqrt{x}-3 =14\)

Example Question #112 : Equations

Set up the following equation:

Seven less than five times a number squared is eight.

Possible Answers:

\(\displaystyle -7-5x^2=8\)

\(\displaystyle 5(7-x^2)=8\)

\(\displaystyle 7-5x^2=8\)

\(\displaystyle 5x^2-7=8\)

\(\displaystyle 5(x^2-7)=8\)

Correct answer:

\(\displaystyle 5x^2-7=8\)

Explanation:

Break up the sentence into parts.

Five times a number squared:  \(\displaystyle 5x^2\)

Seven less than five times a number squared:  \(\displaystyle 5x^2-7\)

Is eight:  \(\displaystyle =8\)

Combine the parts to form the equation.

The answer is:  \(\displaystyle 5x^2-7=8\)

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