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Algebra 1 : Equations / Inequalities

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Example Questions

Example Question #1 : How To Find The Solution To An Equation

$\frac{4^2+6\cdot 9}{4+3(2)}+\frac{7}{14}\cdot\frac{50}{25}-1=$

Possible Answers:

19.8

Correct answer:

Explanation:

1. First simplify the first expression:

$\frac{4^2 +6\cdot 9}{4+3(2)}=\frac{4\cdot 4+54}{4+6}=\frac{16+54}{10}=\frac{70}{10}=7$

2. Then, simplify the next two expressions:

$\frac{7}{14}\cdot\frac{50}{25}=\frac{1}{2}\cdot\frac{2}{1}=1$

3. Finally, add and subtract:

7+1-1=7

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Example Question #1 : How To Find The Solution To An Equation

Solve for x.

$\frac{x^2-x^3-(-x-4)}{\frac{1}{x}+\frac{x}{1}}, x=-2$

Possible Answers:

$\frac{-4}{3}$

$\frac{-28}{5}$

$\frac{-7}{9}$

$\frac{28}{3}$

Correct answer:

$\frac{-28}{5}$

Explanation:

1. First solve for the numerator by plugging in -2 for x:

(-2)^2-(-2)^3-(-(-2)-4)=4+8+2= 14

2. Then, solve the denominator by combining the fractions:

$\frac{1}{x}+\frac{x}{1}= \frac{-1}{2}+\frac{-2}{1}=\frac{-1}{2}+\frac{-4}{2}=\frac{-5}{2}$

3. Finally, "rationalize" the complex fraction by multiplying top and bottom by -2/5:

$\frac{14}{\frac{-5}{2}}\cdot\frac{\frac{-2}{5}}{\frac{-2}{5}}=\frac{\frac{-28}{5}}{1}=\frac{-28}{5}$

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Example Question #1 : How To Find The Solution To An Equation

$\frac{x*7+5*4+1}{y*2+4}=3$

If x/y is equivalent to 12/20, what is the value of x?

Possible Answers:

Correct answer:

Explanation:

$\frac{x*7 +5*4+1}{y*2+4}= \frac{7x +21}{2y +4}=3$

Multiply both sides by the denominator (2y +4) to cancel it:

$\frac{7x +21}{2y +4}*(2y +4)=3*(2y+4)$

7x + 21=6y +12

Now, use substitution to solve for x:

$\frac{x}{y}=\frac{12}{20}-->20x=12y-->10x=6y$

Substitute 10x for 6y in the first equation:

7x+21=(10x)+12

9=3x

3=x

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Example Question #1 : Solving Equations And Inequallities

Solve the following equation for :

2(x + 5) = -4

Possible Answers:

-4.5

Correct answer:

Explanation:

The first step is to distribute (multiply) the 2 through the parentheses:

2(x+5) = -4

2x + 10 = -4

Then isolate on the left side of the equation. Subtract the 10 from the left and right side.

2x + 10 = -4

2x = -14

Finally, to isolate , divide the left side by 2 so that the 2 cancels out. Then divide by 2 on the right side as well.

2x = -14

x = -7

You can verify this answer by plugging the into the original equation.

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Example Question #11 : How To Find The Solution To An Equation

Solve for :

a+bx=d

Possible Answers:

$\frac{b}{a-d}$

$\frac{b}{d-a}$

$\frac{d-a}{b}$

$\frac{a-d}{b}$

None of the other answers

Correct answer:

$\frac{d-a}{b}$

Explanation:

To solve for , isolate it from the other variables. First, subtract from both sides to get

bx=d-a .

Then, divide both sides by to get

$x=\frac{d-a}{b}$

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Example Question #11 : How To Find The Solution To An Equation

Solve for :

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

Possible Answers:

a(c+b)

ac+b

$\frac{(c+b)}{a}$

$\frac{(c-b)}{a}$

a(c-b)

Correct answer:

a(c+b)

Explanation:

To solve for , add to both sides to get

$\frac{x}{a}=c+b$

Then, multiply both sides by to get

x=a(c+b)

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Example Question #134 : Expressions & Equations

Solve for :

9x-2-2x=2x+18

Possible Answers:

Correct answer:

Explanation:

First, combine like terms within the equation to get

7x-2=2x+18 .

Then, add and subtract from both sides to get

5x=20 .

Finally, divide both sides by to get the solution of x=4 .

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Example Question #132 : Equations / Inequalities

Solve for :

2x+4=3(x-1)

Possible Answers:

Correct answer:

Explanation:

First, use the distributive property to simplify the right side of the equation. This gives you

2x+4=3x-3

Then, subtract and add to both sides of the equation to get x=7 .

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Example Question #12 : How To Find The Solution To An Equation

Solve for :

8x-2=2(x+2)

Possible Answers:

Correct answer:

Explanation:

First, use the distributive property to simplify the right side of the equation:

8x-2=2x+4

Then, add and subtract from both sides to get

6x=6

Finally, divide both sides by to get x=1 .

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Example Question #3 : Solving Rational Expressions

Solve for , given the equation below.

$\frac{x + 2}{x - 1} = \frac{2x + 4}{x}$

Possible Answers:

$-2,\; 2$

$2,\; 4$

$4,\; 4$

$-2,\; 4$

No solutions

Correct answer:

$-2,\; 2$

Explanation:

$\frac{x + 2}{x - 1} = \frac{2x + 4}{x}$

Begin by cross-multiplying.

x(x+2) = (x-1)(2x +4)

Distribute the on the left side and expand the polynomial on the right.

x^2+2x=2x^2+4x-2x-4

Combine like terms and rearrange to set the equation equal to zero.

x^2-2x=2x^2+2x-4

0=x^2-4

Now we can isolate and solve for by adding to both sides.

x^2=4

x=2, -2

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Algebra 1 : Equations / Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find The Solution To An Equation

Example Question #1 : How To Find The Solution To An Equation

Example Question #1 : How To Find The Solution To An Equation

Example Question #1 : Solving Equations And Inequallities

Example Question #11 : How To Find The Solution To An Equation

Example Question #11 : How To Find The Solution To An Equation

Example Question #134 : Expressions & Equations

Example Question #132 : Equations / Inequalities

Example Question #12 : How To Find The Solution To An Equation

Example Question #3 : Solving Rational Expressions

All Algebra 1 Resources

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