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SAT II Math I : Solving Equations

Study concepts, example questions & explanations for SAT II Math I

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All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #51 : Solving Equations

Solve for .

x^2=841

Possible Answers:

$\pm39$

$\pm29$

Correct answer:

$\pm29$

Explanation:

This is a one step, one variable problem. This means we want to isolate x on one side of the equation with all other constants on the other side. To do this perform the opposite operation to manipulate the equation

x^2=841

Take the square root on both sides. We also need to consider having a negative answer.

Remember, two negatives multiplied equals a positive number.

$x=\pm29$

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Example Question #56 : Single Variable Algebra

Solve for .

$\sqrt{x+5}=9$

Possible Answers:

Correct answer:

Explanation:

This is a two step, one variable problem. This means we want to isolate x on one side of the equation with all other constants on the other side. To do this perform the opposite operation to manipulate the equation

$\sqrt{x+5}=9$

Square both sides to get rid of the radical.

x+5=9^2=81

Subtract on both sides.

x=76

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Example Question #61 : Single Variable Algebra

Solve for .

4x+15=78

Possible Answers:

16.25

21.75

15.25

15.75

23.23

Correct answer:

15.75

Explanation:

4x+15=78 Subtract on both sides.

4x=63 Divide on both sides.

x=15.75

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Example Question #51 : Solving Equations

Solve for .

2x+37=12

Possible Answers:

11.5

12.5

-12.5

13.5

-11.5

Correct answer:

-12.5

Explanation:

2x+37=12 Subtract on both sides. Since is greater than and is negative, our answer is negative. We treat as a normal subtraction.

2x=-25 Divide on both sides. When dividing with a negative number, our answer is negative.

x=-12.5

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Example Question #52 : Solving Equations

Solve for .

8(x+2)=10x+26

Possible Answers:

Correct answer:

Explanation:

8(x+2)=10x+26 First distribute the to each term in the parantheses.

8x+16=10x+26 Subtract on both sides.

16=2x+26 Subtract on both sides.

-10=2x Divide on both sides.

-5=x

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Example Question #53 : Solving Equations

Solve for .

10x-32=4(x+1)

Possible Answers:

$-\frac{33}{6}$

$-\frac{37}{6}$

$\frac{33}{6}$

Correct answer:

Explanation:

10x-32=4(x+1) Distribute the to each term in the parantheses.

10x-32=4x+4 Add to both sides.

10x=4x+36 Subtract on both sides.

6x=36 Divide on both sides.

x=6

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Example Question #52 : Solving Equations

Solve for .

$\frac{3}{4}(x-8)=36$

Possible Answers:

Correct answer:

Explanation:

There are TWO ways:

Method : (not really preferred)

$\frac{3}{4}(x-8)=36$ Distribute $\frac{3}{4}$ to each term in the parantheses.

$\frac{3x}{4}-6=36$ Add to both sides.

$\frac{3x}{4}=42$ Multiply by the reciprocal $\frac{4}{3}$ on both sides.

x=56

Method : (preferred)

$\frac{3}{4}(x-8)=36$ Multiply by the reciprocal $\frac{4}{3}$ on both sides.

x-8=48 Add to both sides.

x=56

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Example Question #51 : Solving Equations

Solve for .

$\frac{x}{2}=4(x-12)$

Possible Answers:

$\frac{72}{7}$

$\frac{96}{7}$

$\frac{48}{7}$

Correct answer:

$\frac{96}{7}$

Explanation:

$\frac{x}{2}=4(x-12)$ Distribute the to each term in the parantheses.

$\frac{x}{2}=4x-48$ Multiply on both sides.

x=8x-96 Subtract on both sides.

-7x=-96 Divide on both sides.

$x=\frac{96}{7}$

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Example Question #51 : Solving Equations

Solve for .

5(x+1)+3(x-2)=20

Possible Answers:

$\frac{27}{8}$

$\frac{21}{8}$

$\frac{25}{8}$

$\frac{35}{8}$

$\frac{31}{8}$

Correct answer:

$\frac{21}{8}$

Explanation:

5(x+1)+3(x-2)=20 Distribute the to each term in the left parantheses and the to each term in the right parantheses.

5x+5+3x-6=20 Add like terms.

8x-1=20 Add on both sides.

8x=21 Divide on both sides.

$x=\frac{21}{8}$

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Example Question #51 : Solving Equations

Solve for .

$\sqrt{x+1}=10$

Possible Answers:

101

100

Correct answer:

Explanation:

$\sqrt{x+1}=10$ Square both sides to get rid of the radical.

x+1=10^2=100 Subtract on both sides.

x=99

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All SAT II Math I Resources

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SAT II Math I : Solving Equations

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #51 : Solving Equations

Example Question #56 : Single Variable Algebra

Example Question #61 : Single Variable Algebra

Example Question #51 : Solving Equations

Example Question #52 : Solving Equations

Example Question #53 : Solving Equations

Example Question #52 : Solving Equations

Example Question #51 : Solving Equations

Example Question #51 : Solving Equations

Example Question #51 : Solving Equations

All SAT II Math I Resources

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