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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

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Example Question #41 : Solving Equations

Solve for .

(x+3)^2=4

Possible Answers:

$\pm4$

-1, -5

$\pm5$

Correct answer:

-1, -5

Explanation:

(x+3)^2=4 Take the square root on both sides. Remember to account for a negative square root.

$x+3=\pm2$ We will treat as two different equations.

x+3=-2 Subtract on both sides. When adding another negative number, we treat as a sum and add a minus sign in the end. x=-5

x+3=2 Subtract on both sides. Since is greater than and is negative, our answer is negative. We treat as a subtraction problem. x=-1

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Example Question #42 : Solving Equations

Solve for .

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

Possible Answers:

$\pm5$

$\pm2$

2, 5

Correct answer:

Explanation:

$4+\sqrt{6-x}=x$ Let's subtract on both sides. It will be easier to square both sides to get rid of the radical.

6-x=(x-4)^2=x^2-8x+16 This is recognition of a quadratic equation.

x^2-7x+10=0 We need to find two terms that multiply to the c term but add up to the b term.

(x-2)(x-5)=0 Solve individually for zero.

x-2=0 Add on both sides. x=2

x-5=0 Add on both sides. x=5

We need to check our answers.

If x=2 , then $4+\sqrt{6-2}=4+2\neq2$

If x=5 , then $4+\sqrt{6-5}=4+1=5$

Clearly, doesn't work so our final answer is .

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Example Question #51 : Single Variable Algebra

Solve for .

x+234=129

Possible Answers:

363

105

Correct answer:

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+234=129

Subtract 234 on both sides. Since 234 is greater than 129 and is negative, our answer is negative.

We treat as a subtraction problem.

x=-105

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Example Question #52 : Single Variable Algebra

Solve for .

$\frac{x}{5}+334=624$

Possible Answers:

1260

1350

290

1450

Correct answer:

1450

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

$\frac{x}{5}+334=624$

Subtract 334 on both sides.

$\frac{x}{5}=290$

Multiply on both sides.

x=1450

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Example Question #53 : Single Variable Algebra

Solve for .

x-546=278

Possible Answers:

824

786

828

268

634

Correct answer:

824

Explanation:

x-546=278

Add 546 on both sides.

x=824

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Example Question #54 : Single Variable Algebra

Solve for .

$\frac{x}{4}-46=298$

Possible Answers:

344

1376

1286

1776

Correct answer:

1376

Explanation:

$\frac{x}{4}-46=298$

Add on both sides.

$\frac{x}{4}=344$

Multiply on both sides.

x=1376

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Example Question #55 : Single Variable Algebra

Solve for .

45x=-720

Possible Answers:

Correct answer:

Explanation:

45x=-720

Divide on both sides.

When dividing with a negative number, our answer is negative.

x=-16

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Example Question #56 : Single Variable Algebra

Solve for .

9x-34=587

Possible Answers:

Correct answer:

Explanation:

9x-34=587

Add on both sides.

9x=621

Divide on both sides.

x=69

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Example Question #57 : Single Variable Algebra

Solve for .

$\frac{x}{-7}=-469$

Possible Answers:

3283

217

3383

Correct answer:

3283

Explanation:

$\frac{x}{-7}=-469$

Multiply on both sides.

When multiplying with another negative number, our answer is positive.

x=3283

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Example Question #58 : Single Variable Algebra

Solve for .

$\frac{x}{-17}=-69$

Possible Answers:

1173

1383

217

213

671

Correct answer:

1173

Explanation:

$\frac{x}{-17}=-69$

Multiply on both sides.

When multiplying with another negative number, our answer is positive.

x=1173

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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 #41 : Solving Equations

Example Question #42 : Solving Equations

Example Question #51 : Single Variable Algebra

Example Question #52 : Single Variable Algebra

Example Question #53 : Single Variable Algebra

Example Question #54 : Single Variable Algebra

Example Question #55 : Single Variable Algebra

Example Question #56 : Single Variable Algebra

Example Question #57 : Single Variable Algebra

Example Question #58 : Single Variable Algebra

All SAT II Math I Resources

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