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Algebra 1 : Linear 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 #262 : How To Solve Two Step Equations

Solve for

$\frac{x}{5}+3=4$

Possible Answers:

x=3

x=9

x=5

x=-5

Correct answer:

x=5

Explanation:

To solve for we first subtract on both sides

$\frac{x}{5}+3-3=4-3$

$\frac{x}{5}=1$

and then multiply by

$5*\frac{x}{5}=5*1$

and we get

x=5

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Example Question #262 : How To Solve Two Step Equations

Solve: $10x+\frac{1}{10} = 1$

Possible Answers:

$\frac{1}{90}$

$\frac{4}{5}$

$\frac{2}{25}$

$\frac{9}{10}$

$\frac{9}{100}$

Correct answer:

$\frac{9}{100}$

Explanation:

Subtract $\frac{1}{10}$ on both sides.

$10x+\frac{1}{10}-\frac{1}{10} = 1-\frac{1}{10}$

For the right side to be subtracted, their denominators must be common. The least common denominator is ten, and we can rewrite as a ratio of ten over ten.

$10x= \frac{10}{10}-\frac{1}{10}$

Subtract the fractions on the right.

$10x=\frac{9}{10}$

Divide by ten on both sides to isolate . This is the same as multiplying $\frac{1}{10}$ on both sides.

$\frac{1}{10}\cdot10x=\frac{9}{10}\cdot\frac{1}{10}$

The answer is: $\frac{9}{100}$

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Example Question #801 : Algebra 1

Solve: $\frac{3}{4}x +8 = -4$

Possible Answers:

$-\frac{1}{3}$

$-\frac{16}{3}$

$-\frac{13}{4}$

Correct answer:

Explanation:

Subtract eight on both sides to isolate the term with the x-variable.

$\frac{3}{4}x +8 -8= -4-8$

$\frac{3}{4}x=-12$

To isolate the x-variable, we will need to multiply both sides by the reciprocal of the coefficient in front of the x.

$\frac{3}{4}x \cdot \frac{4}{3}=-12 \cdot \frac{4}{3}$

Simplify both sides.

$x= \frac{-48}{3}=-16$

The answer is:

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Example Question #271 : How To Solve Two Step Equations

Solve the following equation: 4x+9 = 41

Possible Answers:

$\frac{25}{2}$

$-\frac{25}{2}$

Correct answer:

Explanation:

Subtract nine on both sides to separate the term with the x variable.

4x+9 -9= 41-9

Simplify both sides.

4x=32

Divide by four on both sides.

$\frac{4x}{4}=\frac{32}{4}$

Simplify both fractions.

x=8

The answer is:

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Example Question #273 : How To Solve Two Step Equations

Solve for :

14q+11=-3

Possible Answers:

q=-1

$q=\frac{-9}{14}$

q=1

q=0

$q=\frac{9}{14}$

Correct answer:

q=-1

Explanation:

To solve this problem you need to get by itself. The first step to do this is to subtract 11 from both sides to get:

14q=-3-11

14q=-14

From here you need to divide both sides by 14 to get a final answer of

q=-1

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Example Question #272 : How To Solve Two Step Equations

An arrow is shot according to the trajectory -x^2=-16

Solve for .

Possible Answers:

x=4

x=4, -4

x=16, -16

No real solution

x=2,-2

Correct answer:

x=4, -4

Explanation:

To simplify this problem you must first divide or multiply both sides by negative one to get:

x^2=16

From here you must square root both sides, but it is important to remember that when you take the square root you get a positive and negative answer.

So:

$x= \sqrt{16}$ so $x=\pm 4$

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Example Question #275 : How To Solve Two Step Equations

Solve the equation: 4x-8 = 32

Possible Answers:

$\frac{1}{10}$

Correct answer:

Explanation:

Isolate the term with the x variable by adding eight on both sides.

4x-8 +8= 32+8

Simplify both sides.

4x=40

Divide by four on both sides.

$\frac{4x}{4}=\frac{40}{4}$

Simplify each fraction on both sides.

The answer is: x=10

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Example Question #271 : How To Solve Two Step Equations

Solve the equation: 3x+6=-17

Possible Answers:

$\frac{23}{3}$

$-\frac{16}{3}$

$\frac{11}{3}$

$-\frac{23}{3}$

$-\frac{11}{3}$

Correct answer:

$-\frac{23}{3}$

Explanation:

Subtract six from both sides of the equation.

3x+6-6=-17-6

Simplify both equations.

3x=-23

Divide by three on both sides.

$\frac{3x}{3}=\frac{-23}{3}$

Simplify both sides.

The answer is: $-\frac{23}{3}$

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Example Question #803 : Algebra 1

Solve the following equation: -6x+8 =-14

Possible Answers:

$-\frac{11}{3}$

$-\frac{3}{11}$

$\frac{11}{3}$

$\frac{3}{11}$

Correct answer:

$\frac{11}{3}$

Explanation:

Subtract eight on both sides.

-6x+8-8 =-14-8

Simplify both sides.

-6x=-22

Divide by negative six on both sides.

$\frac{-6x}{-6}=\frac{-22}{-6}$

The left side will leave by itself. Simplify the right side by common factors.

$x= \frac{-1 \times 2 \times 11}{-1 \times 2 \times 3}$

Cancel the like terms in the numerator and denominator.

The answer is: $\frac{11}{3}$

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Example Question #272 : How To Solve Two Step Equations

Solve the following equation: -6x+9 = -15

Possible Answers:

Correct answer:

Explanation:

Subtract nine on both sides.

-6x+9-9 = -15-9

Simplify both sides.

-6x=-24

Divide by negative six on both sides.

$\frac{-6x}{-6}=\frac{-24}{-6}$

Simplify both sides.

x=4

The answer is:

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #262 : How To Solve Two Step Equations

Example Question #262 : How To Solve Two Step Equations

Example Question #801 : Algebra 1

Example Question #271 : How To Solve Two Step Equations

Example Question #273 : How To Solve Two Step Equations

Example Question #272 : How To Solve Two Step Equations

Example Question #275 : How To Solve Two Step Equations

Example Question #271 : How To Solve Two Step Equations

Example Question #803 : Algebra 1

Example Question #272 : How To Solve Two Step Equations

All Algebra 1 Resources

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