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Algebra 1 : Linear Equations

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Example Questions

Example Question #81 : Proportions

Solve for x:

$\frac{14}{x}=\frac{2}{10}$

Possible Answers:

x=280

x=10

x=28

$x=\frac{14}{5}$

x=70

Correct answer:

x=70

Explanation:

To do this proportion you need to cross-multiply to end up with the equations

2x=140

Then you need to divide both sides by 2 to get by itself and you end up with

x=70

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Example Question #1211 : Algebra 1

Solve the proportion: $\frac{3}{4} = \frac{4}{x}$

Possible Answers:

$\frac{16}{3}$

$\frac{1}{3}$

$\frac{3}{4}$

$\frac{8}{3}$

$\frac{4}{3}$

Correct answer:

$\frac{16}{3}$

Explanation:

In order to solve this proportion, we will need to cross multiply both fractions.

3x=4(4)

Simplify the right side of the equation and divide both sides by three to isolate the x- variable.

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

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Example Question #83 : Proportions

Solve the following proportion: $\frac{4}{x+1} = \frac{2}{x}$

Possible Answers:

$\frac{4}{11}$

$-\frac{3}{5}$

$\frac{3}{4}$

Correct answer:

Explanation:

Cross multiply both fractions:

4x= 2(x+1)

Simplify the right side by distribution.

4x=2x+2

Subtract from both sides.

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

Simplify both sides.

2x=2

Divide by 2 on both sides.

The answer is: x=1

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Example Question #84 : Proportions

Solve the proportion: $\frac{3}{2x} = \frac{11}{5}$

Possible Answers:

$\frac{2}{15}$

$\frac{11}{8}$

$\frac{33}{7}$

$\frac{5}{7}$

$\frac{15}{22}$

Correct answer:

$\frac{15}{22}$

Explanation:

In order to solve for , we will need to cross multiply both fractions.

3(5)= 11(2x)

Simplify both sides.

15=22x

Divide by 22 on both sides.

$\frac{15}{22}=\frac{22x}{22}$

Simplify both fractions.

The answer is: $\frac{15}{22}$

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Example Question #85 : Proportions

Solve the proportion: $\frac{x-1}{3} = \frac{4x}{7}$

Possible Answers:

$-\frac{1}{12}$

$-\frac{5}{12}$

$-\frac{7}{5}$

$-\frac{1}{5}$

$-\frac{7}{12}$

Correct answer:

$-\frac{7}{5}$

Explanation:

To solve the proportion, cross multiply both sides.

(7)(x-1) = (4x)(3)

Distribute to simplify both sides.

7x-7=12x

Subtract on both sides to group the variable.

7x-7-(7x)=12x-(7x)

Simplify both sides.

-7 =5x

Divide both sides by five.

$\frac{-7}{5} =\frac{5x}{5}$

Simplify both sides.

The answer is: $-\frac{7}{5}$

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Example Question #86 : Proportions

Solve the proportion: $\frac{x}{2} = \frac{2x}{3}$

Possible Answers:

$\textup{No solution.}$

$\frac{3}{4}$

$\frac{4}{3}$

Correct answer:

Explanation:

Cross multiply both fractions.

3x = 2(2x)

Simplify the right side.

3x=4x

Do not divide by on both sides, or this will leave us with no solution.

Instead, subtract either or on both sides to group the x-variables.

Subtract on both sides.

3x-3x=4x-3x

Simplify both sides.

0=x

The answer is:

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Example Question #87 : Proportions

Solve the proportion: $\frac{7}{3x} = \frac{3}{7}$

Possible Answers:

$\frac{9}{49}$

$\frac{49}{10}$

$\frac{1}{21}$

$\frac{7}{3}$

$\frac{49}{9}$

Correct answer:

$\frac{49}{9}$

Explanation:

To solve this proportion, cross multiply both fractions.

7(7) = 3(3x)

Simplify both sides of the equation.

49=9x

Divide by nine on both sides.

The answer is: $\frac{49}{9}$

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Example Question #88 : Proportions

Solve the proportion: $\frac{2-x}{2}= \frac{4-x}{5}$

Possible Answers:

$\frac{2}{3}$

$\frac{3}{5}$

$\frac{4}{7}$

$\frac{3}{4}$

$\frac{5}{8}$

Correct answer:

$\frac{2}{3}$

Explanation:

Cross multiply the two fractions.

5(2-x)= 2(4-x)

Distribute the integers through the parentheses.

10-5x = 8-2x

Group the integers on one side, and the $\textup{x-variables}$ on another side. Subtract and add on both sides.

10-5x-(8)+(5x) = 8-2x-(8)+(5x)

Simplify both sides.

2 = 3x

Divide by three on both sides.

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

Simplify the right side.

The answer is: $x=\frac{2}{3}$

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Example Question #89 : Proportions

Solve the proportion: $\frac{x}{x+2} = \frac{6}{7}$

Possible Answers:

$\frac{3}{5}$

$\frac{7}{9}$

Correct answer:

Explanation:

Solve by cross multiplying both fractions.

7x= 6(x+2)

Distribute the right side.

7x=6x+12

Subtract on both sides of the equation.

7x-6x=6x+12-6x

Simplify both sides.

The answer is: x=12

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Example Question #91 : Proportions

Solve the proportion: $\frac{2\sqrt5}{x} = \frac{\sqrt{10}}{2}$

Possible Answers:

$\sqrt5$

$5\sqrt2$

$4\sqrt5$

$2\sqrt5$

$2\sqrt2$

Correct answer:

$2\sqrt2$

Explanation:

Cross multiply both fractions.

$2(2)\sqrt 5 = x\sqrt {10}$

Simplify the left side and divide by square root ten on both sides.

$\frac{4\sqrt 5 }{\sqrt {10}}= \frac{x\sqrt {10}}{\sqrt {10}}$

Cancel out the right side. The equation becomes:

$x=\frac{4\sqrt 5 }{\sqrt {10}}$

Rationalize the denominator by multiplying this fraction by $\frac{\sqrt {10}}{\sqrt {10}}$ .

$x=\frac{4\sqrt{5}}{\sqrt {10}} \cdot \frac{\sqrt {10}}{\sqrt {10}} = \frac{4\sqrt{50}}{10}= \frac{4\cdot 5\sqrt{2}}{10} = \frac{20\sqrt2}{10}$

Divide the coefficients.

The answer is: $2\sqrt2$

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #81 : Proportions

Example Question #1211 : Algebra 1

Example Question #83 : Proportions

Example Question #84 : Proportions

Example Question #85 : Proportions

Example Question #86 : Proportions

Example Question #87 : Proportions

Example Question #88 : Proportions

Example Question #89 : Proportions

Example Question #91 : Proportions

All Algebra 1 Resources

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