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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 #51 : Proportions

Solve for .

$\frac{17}{-5}=\frac{-x}{25}$

Possible Answers:

Correct answer:

Explanation:

$\frac{17}{-5}=\frac{-x}{25}$ Cross-multiply. When multiplying with a negative variable, answer is positive.

5x=425 Divide on both sides.

x=85

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Example Question #52 : Proportions

Solve for .

$\frac{-x}{4}=\frac{-36}{48}$

Possible Answers:

Correct answer:

Explanation:

$\frac{-x}{4}=\frac{-36}{48}$ Cross-multiply. When multiplying with a negative number and variable, answer is negative.

-48x=-144 Divide on both sides. When dividing with another negative number, answer is positive.

x=3

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Example Question #1181 : Algebra 1

Solve for .

$\frac{26}{x}=2$

Possible Answers:

6.5

Correct answer:

Explanation:

$\frac{26}{x}=2$ Multiply on both sides.

26=2x Divide on both sides.

x=13

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Example Question #55 : Proportions

Solve for .

$\frac{1}{x+12}=1$

Possible Answers:

Correct answer:

Explanation:

$\frac{1}{x+12}=1$ Multiply x+12 on both sides.

x+12=1 Subtract on both sides. Since is greater than and is negative, our answer is negative. We treat as subtraction problem.

x=-11

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Example Question #53 : Proportions

Solve for .

$\frac{2}{x+1}=\frac{6}{18}$

Possible Answers:

Correct answer:

Explanation:

$\frac{2}{x+1}=\frac{6}{18}$ Cross-multiply. Don't forget to distribute since the denominator of that fraction is an expression.

6x+6=36 Subtract on both sides.

6x=30 Divide on both sides.

x=5

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Example Question #52 : Proportions

Solve for .

$\frac{x}{x+2}=\frac{6}{10}$

Possible Answers:

Correct answer:

Explanation:

$\frac{x}{x+2}=\frac{6}{10}$ Cross-multiply. Don't forget to distribute since the denominator of that fraction is an expression.

6x+12=10x Subtract on both sides.

12=4x Divide on both sides.

x=3

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Example Question #58 : Proportions

Solve for .

$\frac{x+2}{x-2}=\frac{9}{6}$

Possible Answers:

Correct answer:

Explanation:

$\frac{x+2}{x-2}=\frac{9}{6}$ Cross multply. Don't forget to distribute as the denominators in both fractions are expressions.

6x+12=9x-18 Add on both sides.

6x+30=9x Subtract on both sides.

3x=30 Divide on both sides.

x=10

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Example Question #54 : Proportions

Solve for : $\frac{7}{h}=\frac{5}{7}$

Possible Answers:

$\frac{1}{5}$

$\frac{5}{49}$

$\frac{14}{5}$

$\frac{49}{5}$

Correct answer:

$\frac{49}{5}$

Explanation:

To eliminate the proportion, cross multiply.

The equation becomes:

49=5h

Divide by five on both sides.

$\frac{49}{5}=\frac{5h}{5}$

Cancel the fives on the right side.

The answer is: $h=\frac{49}{5}$

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Example Question #60 : Proportions

Joe biked 12 mi in the first 4 hrs of a bike trip. How far will Joe bike in total if he spend 11hrs on this bike trip? Assume the relationship is directly proportional.

Possible Answers:

24.5mi

33mi

44mi

98mi

132mi

Correct answer:

33mi

Explanation:

To solve this problem, we can set up a proportion to turn our missing value into a single variable. We know that in four hours, he traveled twelve miles. Since the relationship is directly proportional, we need to find how far this rate of travel will take him in eleven hours. Now that this is set up, we can cross multiply to elminate the fractions:

$\frac{12mi}{4hr} = \frac{x}{11hr}$

$12 \times 11 = 132$

$4\times x = 4x$

Set these equal to each other:

132 = 4x Divide both sides by four

x = 33 mi traveled over eleven hours of biking.

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Example Question #61 : Proportions

Solve: $\frac{2}{x}= \frac{6}{5}$

Possible Answers:

$\frac{8}{5}$

$\frac{5}{3}$

$\frac{12}{5}$

$\frac{3}{5}$

$\frac{13}{5}$

Correct answer:

$\frac{5}{3}$

Explanation:

To solve the proportion, we will need to cross multiply.

$2\times 5= 6 \times x$

Simplify both sides.

10=6x

Divide by six on both sides.

$\frac{10}{6}=x$

Reduce the fraction.

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

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #51 : Proportions

Example Question #52 : Proportions

Example Question #1181 : Algebra 1

Example Question #55 : Proportions

Example Question #53 : Proportions

Example Question #52 : Proportions

Example Question #58 : Proportions

Example Question #54 : Proportions

Example Question #60 : Proportions

Example Question #61 : Proportions

All Algebra 1 Resources

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