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Algebra II : Solving Equations

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Example Questions

Example Question #181 : Equations

Solve for :

$75 = -\frac{x}{5} - 5$

Possible Answers:

x = -350

None of the other answers.

x = 350

x = -400

x = 400

Correct answer:

x = -400

Explanation:

$75 = -\frac{x}{5} - 5$

Step 1: Multiply both sides of the equation by 5.

$\rightarrow 375 = -x - 25$

Step 2: Add 25 to both sides of the equation.

$\rightarrow 400 = -x$

Step 3: Divide both sides of the equation by -1.

$\rightarrow x = -400$

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Example Question #51 : Solving Equations

Solve for :

$\frac{5x}{6} - 2 = 5 - \frac{x}{2}$

Possible Answers:

$x = -\frac{21}{4}$

None of the other answers.

x = 6

x = 7

$x = \frac{21}{4}$

Correct answer:

$x = \frac{21}{4}$

Explanation:

$\frac{5x}6 - 2 = 5 - \frac{x}{2}$

Step 1: Multiply both sides of the equation by 6.

$\rightarrow 5x - 12 = 30 - 3x$

Step 2: Add to both sides of the equation, and add 12 to both sides of the equation.

$\rightarrow 8x = 42$

Step 3: Divide both sides of the equation by 8.

$\rightarrow x = \frac{21}{4}$

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Example Question #52 : Solving Equations

Solve for :

$-24 - \frac{2x}{5} = 100 + 3x$

Possible Answers:

$x = -\frac{620}{17}$

$x = \frac{620}{17}$

None of the other answers.

$x = -\frac{524}{17}$

$x = \frac{524}{17}$

Correct answer:

$x = -\frac{620}{17}$

Explanation:

$-24 - \frac{2x}{5} = 100 + 3x$

Step 1: Multiply both sides of the equation by 5.

$\rightarrow -120 - 2x = 500 + 15x$

Step 2: Add to both sides of the equation, and subtract 500 from both sides of the equation.

$\rightarrow -620 = 17x$

Step 3: Divide both sides of the equation by 17.

$\rightarrow x = -\frac{620}{17}$

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Example Question #181 : Equations

Solve:

2(3x-1)+4=20

Possible Answers:

x=10

x=13

x=-3

x=1

x=3

Correct answer:

x=3

Explanation:

Take this equation step by step. First, I would do the distributive property so that the equation looks like:

6x-2+4=20 .

Next, combine like terms:

6x+2=20 .

Subtract 2 from both sides so that you get

6x=18 .

Then, divide by 6 so that x=3.

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Example Question #53 : Solving Equations

Find .

2(x+4)=10

Possible Answers:

x=1

x=-1

x=10

x=8

x=2

Correct answer:

x=1

Explanation:

To find you must isolate the variable on one side of the equation. In this case, start by dividing both sides of the equation by .

$\frac{2(x+4)}{2}=\frac{10}{2}$

x+4=5

Then, subtract from each side.

x+4-4=5-4

x=5-4

This will leave you with the answer x=1 .

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Example Question #181 : Equations

Solve this equation: 3x-3=9-(12x-3)

Possible Answers:

x=15/9

x=3

x=3/5

x=9/15

x=1

Correct answer:

x=1

Explanation:

First things first, always do the same operation to each side; never subtract only from one side. We do this because of the equal sign in the middle (each side must remain equal to each other).

3x-3=9-(12x-3)

First distribute the negative sign on the right side:

3x-3=9-12x+3)

Now get all the x's on one side by adding 12 to BOTH sides:

15x-3=9+3

Simplify the right side:

15x-3=12

Isolate the X variable:

15x=15

Once more, but this time by division:

x=1

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Example Question #51 : Solving Equations

Solve the following equation:

-12=4+5x-20-3x

Possible Answers:

$x=\frac{1}{2}$

$x=\frac{7}{2}$

x=2

$x=\frac{6}{7}$

x=-14

Correct answer:

x=2

Explanation:

Collect like terms and solve for x.

-12=4+5x-20-3x

-12-4+20=5x-3x

4=2x

x=2

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Example Question #53 : Solving Equations

Solve for :

$\frac{ 15 } { 2x + 7 } = 3$

Possible Answers:

$\frac{ 4}{3}$

Correct answer:

Explanation:

To solve, we first need to get x out of the denominator so that we can start to isolate it.

Multiply both sides by 2x+7 :

3(2x + 7 ) = 15

Divide both sides by 3.

2 x + 7 = 5

Subtract 7 from both sides.

2 x = -2

Divide by 2

x = -1

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Example Question #53 : Solving Equations

-2(x + 1 ) = -8

Possible Answers:

4.5

Correct answer:

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

-2(x + 1 ) = -8

First divide both sides by -2.

x + 1 = 4

Next, subtract 1 from both sides.

x= 3

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Example Question #54 : Solving Equations

Solve for :

$2 = \frac{ 2x - 4 }{ 3 }$

Possible Answers:

$\frac{ 1}{2}$

Correct answer:

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

$2 = \frac{ 2x - 4 }{ 3 }$

First multiply both sides by 3.

6 = 2x - 4 .

Next, add 4 to both sides.

10 = 2x

Finally, divide both sides by 2.

5 = x

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Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #181 : Equations

Example Question #51 : Solving Equations

Example Question #52 : Solving Equations

Example Question #181 : Equations

Example Question #53 : Solving Equations

Example Question #181 : Equations

Example Question #51 : Solving Equations

Example Question #53 : Solving Equations

Example Question #53 : Solving Equations

Example Question #54 : Solving Equations

All Algebra II Resources

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