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Algebra 1 : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Linear / Rational / Variable Equations

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:

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

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

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

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

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 #12 : How To Find The Solution To An Equation

Solve for :

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

Possible Answers:

a(c-b)

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

a(c+b)

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

ac+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 #12 : Linear / Rational / Variable 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 #11 : How To Find The Solution To An Equation

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 #14 : 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 #11 : How To Find The Solution To An Equation

Solve for , given the equation below.

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

Possible Answers:

$-2,\; 4$

$2,\; 4$

No solutions

$4,\; 4$

$-2,\; 2$

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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Example Question #14 : How To Find The Solution To An Equation

Simplify the result of the following steps, to be completed in order:

1. Add to

2. Multiply the sum by

3. Add to the product

4. Subtract from the sum

Possible Answers:

29x + 13y

28x + 12y

28x + 13y

28x -13y

28x + 11y

Correct answer:

28x + 13y

Explanation:

Step 1: 7x + 3y

Step 2: 4 * (7x + 3y) = 28x + 12y

Step 3: 28x + 12y + x = 29x + 12y

Step 4: 29x + 12y – (x – y) = 29x + 12y – x + y = 28x + 13y

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

2x + 6y = 44

What is x + 3y + 33 ?

Possible Answers:

The answer cannot be determined.

Correct answer:

Explanation:

The key to solving this question is noticing that we can factor out a 2:

2x + 6y = 44 is the same as 2(x + 3y) = 44.

Therefore, x + 3y = 22.

In this case, x + 3y + 33 is the same as 22 + 33, or 55.

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Example Question #3 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for .

5x+15=10y

5y+x=18

Possible Answers:

y=3

x=5

x=3

x=15

Cannot be determined

Correct answer:

x=3

Explanation:

Subtract x from both sides of the second equation.

5y+x=18

5y=18-x

Divide both sides by to get $y=\frac{18-x}{5}$ .

Plug in y to the other equation.

5x+15=10y

$5x+15= 10*\frac{18-x}{5}$

Divide 10 by 5 to eliminate the fraction, yielding 5x+15=2(18-x) .

Distribute the 2 to get 5x+15=36-2x .

Add to each side, and subtract 15 from each side to get 7x=21 .

Divide both sides by 7 to get $\frac{x}{7}=\frac{21}{7}$ , which simplifies to x=3 .

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Algebra 1 : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : Linear / Rational / Variable Equations

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

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

Example Question #12 : Linear / Rational / Variable Equations

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

Example Question #14 : How To Find The Solution To An Equation

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

Example Question #14 : How To Find The Solution To An Equation

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

Example Question #3 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

All Algebra 1 Resources

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