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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #61 : Solving Equations

Solve for x: bx-cx=x-2

Possible Answers:

$x=\frac{-2}{b-c-1}$

$x=\frac{b-c-1}{2}$

Cannot be solved

$x=\frac{-1}{b-c}$

$x=\frac{b-c-1}{-2}$

Correct answer:

$x=\frac{-2}{b-c-1}$

Explanation:

bx-cx=x-2

Subtract to move all x terms to the same side:

bx-cx-x=-2

Factor out an x:

x(b-c-1)=-2

Divide to isolate x completely:

$\mathbf{x=\frac{-2}{b-c-1}}$

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Example Question #71 : Solving Equations

Solve for x: $\sqrt{2x-4x}=\sqrt{x-2}$

Possible Answers:

$x=\frac{3}{2}$

x=-2

$x=\frac{2}{3}$

x=2

x=1

Correct answer:

$x=\frac{2}{3}$

Explanation:

$\sqrt{2x-4x}=\sqrt{x-2}$

Square both sides to remove the radicals:

2x-4x=x-2

Combine x terms:

-2x=x-2

Combine x terms to one side by subtracting:

-3x=-2

Isolate x completely:

$x=\frac{2}{3}$

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Example Question #72 : Solving Equations

Find the solution to the following equation.

9x+23=59

Possible Answers:

x=4

x=36

x=40.5

x=-4

Correct answer:

x=4

Explanation:

Find the solution to the following equation.

9x+23=59

To find the solution of this equation, we need to find the value for x, which makes the given equation true.

We do this by working backwards and manipulating the equation.

The easiest first step would probably be to subtract 23 from both sides:

9x+23(-23)=59(-23)

By doing so, we can simplify the equation to get:

9x=36

Next, simply divide both sides by 9 to get the answer!

$9x\div 9=36\div9$

So we get:

x=4

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Example Question #2391 : Algebra Ii

Given the following equation, find the value of

355=7b+12

Possible Answers:

343

117649

Correct answer:

117649

Explanation:

Given the following equation, find the value of

355=7b+12

To find the value of , we first need to find the value of b

Let's begin by subtracting 12

355(-12)=7b+12(-12)

Simplify

343=7b

Finally, divide by 7

$b=\frac{343}{7}=49$

But, we need

So:

b^3=49^3=117649

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Example Question #201 : Equations

27x-9=-18

Possible Answers:

None of these

x=3

$x=\frac{1}{3}$

x=-3

$x=-\frac{1}{3}$

Correct answer:

$x=-\frac{1}{3}$

Explanation:

27x-9=-18

Add 9 to both sides:

27x=-9

Divide both sides by 27:

$\mathbf{x=-\frac{1}{3}}$

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Example Question #201 : Equations

27x-9=-18

Possible Answers:

None of these

x=3

$x=\frac{1}{3}$

x=-3

$x=-\frac{1}{3}$

Correct answer:

$x=-\frac{1}{3}$

Explanation:

27x-9=-18

Add 9 to both sides:

27x=-9

Divide both sides by 27:

$\mathbf{x=-\frac{1}{3}}$

Report an Error

Example Question #75 : Solving Equations

I sell bagels for cents plus ten cents for the bag it comes in. How many bagels can u buy if you brought $ 3.35 ?

Possible Answers:

Correct answer:

Explanation:

Let's set-up an equation.

.25x+.10=3.35 represents the amount of bagels. After subtracting on both sides and dividing by 0.25 , our answer should be bagels.

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Example Question #2393 : Algebra Ii

Bob rides in a NYC taxi in which the opening fare is $ 2.00 . The taxi charges cents for every $\frac{1}{5}$ of a mile. How far did Bob go if the fare costs $ 21.80 ?

Possible Answers:

14.6

13.2

12.8

Correct answer:

13.2

Explanation:

Let's set-up an equation.

2+0.3x=21.80 how many fifth miles the taxi charges. After subtracting on both sides and dividing by 0.3 , our answer should be . But of course, this is not the final answer because that's how many times the taxi charges for every fifth mile. So $66*\frac{1}{5}=13.2$ miles.

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Example Question #77 : Solving Equations

A gas tank holds gallons. A car uses $\frac{1}{40}$ of a gallon per mile. How many gallons is left if the person travelled 600 miles?

Possible Answers:

Correct answer:

Explanation:

Since the person has traveled 600 miles and each mile uses $\frac{1}{40}$ gallon, we can determine how many gallons used. $\frac{600}{40}=15$ gallons used. Since a tank holds gallons, we subtract and to get gallons.

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Example Question #211 : Equations

Josh weighs 300 pounds. He goes on a diet and loses pounds every days. How long does it take for him to drop to 180 pounds?

Possible Answers:

120

300

360

Correct answer:

300

Explanation:

Let's set-up an equation.

300-2x=180 represents how many times he lost the pounds. By subtracting 300 on both sides and dividing by later, we get . That's not our answer as he loses weight every five days. So we do 60*5=300 days.

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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #61 : Solving Equations

Example Question #71 : Solving Equations

Example Question #72 : Solving Equations

Example Question #2391 : Algebra Ii

Example Question #201 : Equations

Example Question #201 : Equations

Example Question #75 : Solving Equations

Example Question #2393 : Algebra Ii

Example Question #77 : Solving Equations

Example Question #211 : Equations

All Algebra II Resources

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