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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

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All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #32 : How To Solve For A Variable As Part Of A Fraction

Solve for .

$\frac{5}{3x-8}=\frac{7}{3}$

Possible Answers:

$-\frac{71}{21}$

$-\frac{21}{71}$

$\frac{71}{21}$

$\frac{21}{71}$

Correct answer:

$\frac{71}{21}$

Explanation:

First, cross-multiply.

3(5)=7(3x-8)

Now, simplify and solve for .

15=21x-56

71=21x

$x=\frac{71}{21}$

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Example Question #1251 : Algebra

Solve for .

$\frac{7x}{2}=\frac{5}{4}$

Possible Answers:

$\frac{7}{12}$

$\frac{1}{4}$

$\frac{2}{13}$

$\frac{5}{14}$

Correct answer:

$\frac{5}{14}$

Explanation:

First, cross-multiply.

7x(4)=5(2)

Now, simplify and solve for .

28x=10

$x=\frac{10}{28}=\frac{5}{14}$

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Example Question #31 : How To Solve For A Variable As Part Of A Fraction

Solve for .

$\frac{4x}{3}=\frac{9}{5}$

Possible Answers:

$\frac{20}{27}$

$\frac{4}{7}$

$\frac{27}{20}$

$\frac{2}{5}$

Correct answer:

$\frac{27}{20}$

Explanation:

First, cross-multiply.

5(4x)=27

Now, solve for .

20x=27

$x=\frac{27}{20}$

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Example Question #1251 : Algebra

Solve for .

$\frac{x}{7}=\frac{2}{3}$

Possible Answers:

$\frac{14}{3}$

$\frac{8}{7}$

$\frac{12}{3}$

$\frac{17}{4}$

Correct answer:

$\frac{14}{3}$

Explanation:

First, cross-multiply.

7(2)=3x

Now, solve for .

$x=\frac{14}{3}$

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Example Question #33 : How To Solve For A Variable As Part Of A Fraction

Solve for .

$\frac{4x}{5}=\frac{2}{6}$

Possible Answers:

$\frac{1}{3}$

$\frac{7}{12}$

$\frac{5}{7}$

$\frac{5}{12}$

Correct answer:

$\frac{5}{12}$

Explanation:

First, cross-multiply.

24x=10

Now, solve for .

$x=\frac{10}{24}$

Simplify.

$\frac{5}{12}$

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Example Question #33 : How To Solve For A Variable As Part Of A Fraction

Solve for .

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

Possible Answers:

$\frac{1}{2}$

$\frac{2}{3}$

Correct answer:

Explanation:

First, cross-multiply.

10x-20=10

Now, solve for .

10x=30

$x=\frac{30}{10}=3$

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Example Question #3111 : Act Math

Solve for .

$\frac{4x-2}{3}=\frac{4}{3}$

Possible Answers:

$\frac{7}{2}$

$\frac{3}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

First, cross-multiply.

3(4x-2)=12

Simplify.

12x-6=12

Solve for .

12x=18

$x=\frac{18}{12}=\frac{3}{2}$

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Example Question #3112 : Act Math

Solve for .

$\frac{3}{5-x}=\frac{2}{3}$

Possible Answers:

$\frac{3}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

First, cross-multiply.

9=10-2x

Now, solve for .

-1=-2x

$\frac{1}{2}=x$

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Example Question #91 : Algebraic Fractions

Solve for

$\frac{5x+1}{2} = \frac{-3x}{6}$

Possible Answers:

$\frac{12}{18}$

$-\frac{12}{18}$

$-\frac{1}{6}$

Correct answer:

$-\frac{1}{6}$

Explanation:

To solve these types of problems, you need to cross multiply the fractions

$\frac{5x+1}{2}=\frac{-3x}{6} \rightarrow (5x+1)6 = 2*-3x$ .

Then, all we need to do is distribute the , combine like terms, and solve the algebraic equation.

$30x + 6 = -6x \rightarrow 36x = -6 \rightarrow x = -\frac{1}{6}$ .

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Example Question #92 : Algebraic Fractions

Solve for :

$\frac{x+7}{4}=\frac{3}{2}$

Possible Answers:

$\frac{3}{2}$

$\frac{2}{3}$

Correct answer:

Explanation:

Cross-multiply: 2(x+7)=12

Distribute: 2x+14=12

Solve for x: 2x=-2

x=-1

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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #32 : How To Solve For A Variable As Part Of A Fraction

Example Question #1251 : Algebra

Example Question #31 : How To Solve For A Variable As Part Of A Fraction

Example Question #1251 : Algebra

Example Question #33 : How To Solve For A Variable As Part Of A Fraction

Example Question #33 : How To Solve For A Variable As Part Of A Fraction

Example Question #3111 : Act Math

Example Question #3112 : Act Math

Example Question #91 : Algebraic Fractions

Example Question #92 : Algebraic Fractions

All ACT Math Resources

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