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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #51 : Equations

Set up the following equation: The square root of a three times a number cubed is eight.

Possible Answers:

$x^2\sqrt{3x}=8$ $\displaystyle x^2\sqrt{3x}=8$

$\sqrt{27x}=8$ $\displaystyle \sqrt{27x}=8$

$\sqrt{(3x)^3}=8$ $\displaystyle \sqrt{(3x)^3}=8$

$3\sqrt{x^3}=8$ $\displaystyle 3\sqrt{x^3}=8$

$\sqrt{3x^3}=8$ $\displaystyle \sqrt{3x^3}=8$

Correct answer:

$\sqrt{3x^3}=8$ $\displaystyle \sqrt{3x^3}=8$

Explanation:

Split up the sentence into parts.

A number cubed: x^3 $\displaystyle x^3$

Three times a number cubed: 3x^3 $\displaystyle 3x^3$

The square root of a three times a number cubed: $\sqrt{3x^3}$ $\displaystyle \sqrt{3x^3}$

Is eight: $\displaystyle =8$

Combine the terms to form the equation.

The answer is: $\sqrt{3x^3}=8$ $\displaystyle \sqrt{3x^3}=8$

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Example Question #51 : Equations

Set up the equation:

The difference of six and a number squared is four.

Possible Answers:

$\sqrt{x-6}=4$ $\displaystyle \sqrt{x-6}=4$

x^2-6=4 $\displaystyle x^2-6=4$

6-x^2=4 $\displaystyle 6-x^2=4$

$\displaystyle (6-x)^2=4$

$\displaystyle (x-6)^2=4$

Correct answer:

6-x^2=4 $\displaystyle 6-x^2=4$

Explanation:

Write the following sentence by parts.

A number squared: x^2 $\displaystyle x^2$

The difference of six and a number squared: 6-x^2 $\displaystyle 6-x^2$

Is four: $\displaystyle =4$

Combine the parts to write an equation.

The answer is: 6-x^2=4 $\displaystyle 6-x^2=4$

Report an Error

Example Question #139 : How To Find F(X)

Set up the following equation: Three less than the square of a number is eleven.

Possible Answers:

$\displaystyle x^2-3=11$

$\displaystyle -3-x^2=11$

$\displaystyle 3-x^2=11$

$\displaystyle (3-x)^2=11$

$\displaystyle (x-3)^2=11$

Correct answer:

$\displaystyle x^2-3=11$

Explanation:

Split up the question into parts.

The square of a number: x^2 $\displaystyle x^2$

Three less than the square of a number: x^2-3 $\displaystyle x^2-3$

Is eleven: =11 $\displaystyle =11$

Combine the terms.

The answer is: $\displaystyle x^2-3=11$

Report an Error

Example Question #51 : Setting Up Equations

Set up the equation: Four more than seven times a number is fifty.

Possible Answers:

$\displaystyle 7(x+4)=50$

$\displaystyle 4(x+7)=50$

7x+4=50 $\displaystyle 7x+4=50$

4x+7=50 $\displaystyle 4x+7=50$

$\displaystyle (x+4)^7=50$

Correct answer:

7x+4=50 $\displaystyle 7x+4=50$

Explanation:

Break up the sentence into parts.

Seven times a number: $\displaystyle 7x$

Four more than seven times a number: 7x+4 $\displaystyle 7x+4$

Is fifty: =50 $\displaystyle =50$

Combine the terms to form the equation.

The answer is: 7x+4=50 $\displaystyle 7x+4=50$

Report an Error

Example Question #52 : Equations

Set up the equation: Six less than four times a number squared is eight.

Possible Answers:

$\displaystyle 4(x^2-6)=8$

$\displaystyle 6-4x^2=8$

$\displaystyle (4x-6)^2=8$

$\displaystyle 4(x-6)^2=8$

$\displaystyle 4x^2-6=8$

Correct answer:

$\displaystyle 4x^2-6=8$

Explanation:

Split up the sentence into parts.

Four times a number squared: 4x^2 $\displaystyle 4x^2$

Six less than four times a number squared: 4x^2-6 $\displaystyle 4x^2-6$

Is eight: $\displaystyle =8$

Combine the terms to form an equation.

The answer is: $\displaystyle 4x^2-6=8$

Report an Error

Example Question #402 : Basic Single Variable Algebra

Set up the equation: Four less than a number is at least sixty.

Possible Answers:

x-4>60 $\displaystyle x-4>60$

$x-4\geq60$ $\displaystyle x-4\geq60$

$x-4\leq60$ $\displaystyle x-4\leq60$

$4-x\geq60$ $\displaystyle 4-x\geq60$

$x\geq56$ $\displaystyle x\geq56$

Correct answer:

$x-4\geq60$ $\displaystyle x-4\geq60$

Explanation:

Break up the sentence into parts. Let the number be $\displaystyle x$ .

Four less than a number: x-4 $\displaystyle x-4$

Is at least sixty: $\geq60$ $\displaystyle \geq60$

Combine the parts to form the inequality.

The answer is: $x-4\geq60$ $\displaystyle x-4\geq60$

Report an Error

Example Question #52 : Setting Up Equations

Set up the equation: Sixteen less than eight times a number cubed is nine.

Possible Answers:

$\displaystyle 8(x-16)^3=9$

$\displaystyle (8x-16)^3=9$

$\displaystyle (8x)^3-16=9$

$\displaystyle 8x^3-16=9$

$\displaystyle 8(x^3-16)=9$

Correct answer:

$\displaystyle 8x^3-16=9$

Explanation:

Break up the sentence into parts.

A number cubed: x^3 $\displaystyle x^3$

Eight times a number cubed: 8x^3 $\displaystyle 8x^3$

Sixteen less than eight times a number cubed: 8x^3-16 $\displaystyle 8x^3-16$

Is nine: $\displaystyle =9$

Combine the parts to form an equation.

The answer is: $\displaystyle 8x^3-16=9$

Report an Error

Example Question #401 : Basic Single Variable Algebra

Set up the equation: Eight less than three times a number is negative four.

Possible Answers:

3x-8=-4 $\displaystyle 3x-8=-4$

$\displaystyle 3(8-x)=-4$

$\displaystyle 3(x-8)=-4$

3x=-4 $\displaystyle 3x=-4$

8-3x=-4 $\displaystyle 8-3x=-4$

Correct answer:

3x-8=-4 $\displaystyle 3x-8=-4$

Explanation:

Break up this sentence into parts:

Three times a number: $\displaystyle 3x$

Eight less than three times a number: 3x-8 $\displaystyle 3x-8$

Is negative four: =-4 $\displaystyle =-4$

Combine the parts to form the equation.

The answer is: 3x-8=-4 $\displaystyle 3x-8=-4$

Report an Error

Example Question #57 : Equations

Set up the equation: Sixteen less than twice a number is ninety.

Possible Answers:

$\displaystyle -16-2x=90$

$\displaystyle 2(16-x)=90$

$\displaystyle 2(x-16)=90$

$\displaystyle 2x-16=90$

$\displaystyle 16-2x=90$

Correct answer:

$\displaystyle 2x-16=90$

Explanation:

Break up the sentence into parts.

Twice a number: $\displaystyle 2x$

Sixteen less than twice a number: 2x-16 $\displaystyle 2x-16$

Is ninety: $\displaystyle 90$

Combine the parts to form the equation.

The answer is: $\displaystyle 2x-16=90$

Report an Error

Example Question #52 : Equations

Set up the following equation: Nine less than eight times a number is seventeen.

Possible Answers:

$\displaystyle 8(x-9)=17$

8x-9=17 $\displaystyle 8x-9=17$

$\displaystyle 8(9-x)=17$

9-8x=17 $\displaystyle 9-8x=17$

Correct answer:

8x-9=17 $\displaystyle 8x-9=17$

Explanation:

Break up the sentence into parts.

Eight times a number: $\displaystyle 8x$

Nine less than eight times a number: 8x-9 $\displaystyle 8x-9$

Is seventeen: =17 $\displaystyle =17$

Combine the last two parts to set up the equation.

The answer is: 8x-9=17 $\displaystyle 8x-9=17$

Report an Error

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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #51 : Equations

Example Question #51 : Equations

Example Question #139 : How To Find F(X)

Example Question #51 : Setting Up Equations

Example Question #52 : Equations

Example Question #402 : Basic Single Variable Algebra

Example Question #52 : Setting Up Equations

Example Question #401 : Basic Single Variable Algebra

Example Question #57 : Equations

Example Question #52 : Equations

All Algebra II Resources

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