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Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #232 : Equations

Solve for .

$\frac{2}{3}(x+3)=24$

Possible Answers:

Correct answer:

Explanation:

There are TWO ways:

Method : (not so preferred)

$\frac{2}{3}(x+3)=24$ Distribute $\frac{2}{3}$ .

$\frac{2x}{3}+2=24$ Subtract on both sides.

$\frac{2x}{3}=22$ Multiply $\frac{3}{2}$ on both sides.

x=33

Method : (preferred)

$\frac{2}{3}(x+3)=24$ Multiply $\frac{3}{2}$ on both sides.

x+3=36 Subtract on both sides.

x=33

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Example Question #233 : Equations

Solve for .

$\frac{2}{3}=\frac{x}{12}$

Possible Answers:

Correct answer:

Explanation:

$\frac{2}{3}=\frac{x}{12}$ Cross-multiply.

3x=24 Divide on both sides.

x=8

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Example Question #234 : Equations

Solve for .

$\frac{4}{x+12}=\frac{10}{85}$

Possible Answers:

32.8

24.8

35.2

Correct answer:

Explanation:

$\frac{4}{x+12}=\frac{10}{85}$ Cross-multiply. Remember the multiplies the whole expression.

10(x+12)=4*85 Distribute.

10x+120=340 Subtract 120 on both sides.

10x=220 Divide on both sides.

x=22

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Example Question #235 : Equations

Solve

2x+5=7

Possible Answers:

x=2

x=1

x=4

x=6

x=-1

Correct answer:

x=1

Explanation:

Solve 2x+5=7 by:

The objective is to solve the equation to find what is equal to, so we need to have a value.

First subtract 5 from both sides , and we will get:

2x=2

Divide both sides by 2 and the solution is:

x=1

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Example Question #236 : Equations

Solve:

4x+18=2x-4

Possible Answers:

x=-11

x=11

x=-7

x=10

x=-12

Correct answer:

x=-11

Explanation:

The objective is to solve the equation to find what is equal to, so we need to have a value.

4x+18=2x-4

1. Subtract from both sides, and we will have:

2x+18=-4

2. Subtract 18 from both sides, and we will have:

2x=-22

3. Divide both sides of the equation by 2 and the solution is:

x=-11

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Example Question #237 : Equations

Solve:

5x + 14 -2(x+4)=x+3(x+1)-(x-3)

Possible Answers:

No solution

x=22

None of the above

All real numbers

x=1

Correct answer:

All real numbers

Explanation:

To solve:

5x + 14 -2(x+4)=x+3(x+1)-(x-3)

1. First clear the parentheses.

5x + 14 -2x-8=x+3x+3-x+3

2. Add the variables.

3x+ 14-8=3x+3+3

3. Add the integers.

3x+ 6=3x+6

4. Subtract from each side.

6=6

Which is always true, so x can be all real numbers.

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Example Question #2421 : Algebra Ii

Solve the following equation:

$\small x^2+64=-36$

Possible Answers:

$\small x= 0$

$\small x=-10$

$\small x=10, x=-10$

$\small x=10$

No solution

Correct answer:

No solution

Explanation:

To simplify this you need to isolate x by subtracting 64 from both sides then taking the square root to get:

$\small \sqrt{-100}$

you cannot take the square root of a negative number so you answer is no solution.

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Example Question #231 : Equations

Solve the following equation:

$\small -12x+36=96$

Possible Answers:

$\small x=-5$

$\small x=-6$

$\small x=6$

$\small x=5$

$\small x=-12$

Correct answer:

$\small x=-5$

Explanation:

This is a simple two step problem in which you need to isolate "x" The first step is to subtract the 36 from both sides. Upon doing this you get:

$\small -12x=60$

The next step is to divide by -12 to get "x" by itself.

Your final answer is:

$\small x=-5$

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Example Question #240 : Equations

Solve the following equation for ,

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

Possible Answers:

$x = \frac{8}{11}$

$x = \frac{2}{11}$

$x = -\frac{2}{11}$

$x =- \frac{11}{8}$

x = 3

Correct answer:

$x = \frac{8}{11}$

Explanation:

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

We can start by multiplying both sides by the denominator

$4\times (3x-2)=4\times \frac{x}{4}$

12x - 8 = x

Isolate terms with on one side of the equation,

12x -x = 8

Collect terms and solve,

11x = 8

$x = \frac{8}{11}$

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Example Question #101 : Solving Equations

Solve for a.

$\frac{a-7}{a+3}=\frac{a-9}{a-3}$

Possible Answers:

a=12

a=15

a=10

a=8

a=9

Correct answer:

a=12

Explanation:

Step 1: Cross multiply

(a-7)(a-3)=(a-9)(a+3)

Step 2: FOIL the polynomials

a^2-10a+21=a^2-6a-27

Step 3: Combine like terms & solve

48=4a

12=a

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Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #232 : Equations

Example Question #233 : Equations

Example Question #234 : Equations

Example Question #235 : Equations

Example Question #236 : Equations

Example Question #237 : Equations

Example Question #2421 : Algebra Ii

Example Question #231 : Equations

Example Question #240 : Equations

Example Question #101 : Solving Equations

All Algebra II Resources

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