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Algebra 1 : Algebra 1

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 #1201 : Algebra 1

Solve the proportion: $\frac{6}{x} = \frac{1}{7}$

Possible Answers:

$\frac{7}{6}$

$\frac{6}{7}$

Correct answer:

Explanation:

Cross multiply the fractions.

(6)(7)=(x)(1)

Simplify both sides.

x=42

The answer is:

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Example Question #1202 : Linear Equations

Solve the proportion: $\frac{2x+3}{6} = \frac{4x-3}{5}$

Possible Answers:

$-\frac{33}{14}$

$\frac{14}{33}$

$\frac{33}{8}$

$\frac{33}{14}$

$-\frac{14}{33}$

Correct answer:

$\frac{33}{14}$

Explanation:

Cross multiply the fractions.

(2x+3)(5)=(4x-3)(6)

Use the distributive property to simplify the equation.

10x+15= 24x-18

In order to group the terms, subtract 10x on both sides, and add 18 on both sides.

10x+15 -(10x)+[18]= 24x-18-(10x)+[18]

Simplify the equation.

33 = 14x

Divide by 14 on both sides and simplify.

$\frac{33}{14} = \frac{14x}{14}$

$x=\frac{33}{14}$

The answer is: $\frac{33}{14}$

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Example Question #1203 : Linear Equations

Solve the proportion: $\frac{3}{8x}= \frac{8}{3}$

Possible Answers:

$\frac{3}{8}$

$\frac{8}{3}$

$\frac{64}{9}$

$\frac{9}{64}$

Correct answer:

$\frac{9}{64}$

Explanation:

In order to solve for the unknown variable, cross multiply both fractions.

(3)(3)= (8)(8x)

Simplify both sides.

9=64x

Divide by 64 on both sides.

$x= \frac{9}{64}$

The answer is: $\frac{9}{64}$

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Example Question #1202 : Algebra 1

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

Possible Answers:

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{4}{5}$

Correct answer:

Explanation:

Cross multiply the two fractions.

2(x+2)=3x

Distribute the left side.

2x+4=3x

Subtract from both sides.

2x+4-2x=3x-2x

Simplify both sides.

4=x

The answer is:

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Example Question #76 : Proportions

Solve the proportion: $\frac{8}{7x} =\frac{3}{4}$

Possible Answers:

$\frac{28}{11}$

$\frac{32}{21}$

$\frac{7}{3}$

$\frac{6}{5}$

$\frac{3}{7}$

Correct answer:

$\frac{32}{21}$

Explanation:

Cross multiply the two fractions.

8(4)= (7x)(3)

Simplify both sides.

32 = 21x

Divide by 21 on both sides to isolate the x-variable.

$\frac{32}{21} =\frac{ 21x}{21}$

Reduce the right side of the equation. The left side of the equation is irreducible.

The answer is: $x=\frac{32}{21}$

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Example Question #1203 : Algebra 1

Solve the proportion: $\frac{3}{4} = \frac{2(x+2)}{3}$

Possible Answers:

$-\frac{7}{8}$

$\frac{2}{3}$

$\frac{1}{8}$

Correct answer:

$-\frac{7}{8}$

Explanation:

Cross multiply the two fractions.

(3)(3)= 2(4)(x+2)

Simplify both sides of the equation.

9=8x+16

Subtract 16 from both sides and simplify the equation.

9-16=8x+16-16

-7=8x

Divide by eight on both sides.

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

The answer is: $x=-\frac{7}{8}$

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Example Question #78 : Proportions

Solve the proportion: $\frac{2}{x+1} = \frac{3}{x+2}$

Possible Answers:

$-\frac{3}{2}$

$-\frac{2}{3}$

$\frac{3}{4}$

Correct answer:

Explanation:

To solve the proportion, cross multiply both sides of the equation.

2(x+2)=3(x+1)

Distribute the terms to simplify.

2x+4=3x+3

Subtract from both sides.

4=x+3

Subtract three from both sides.

x=1

The answer is:

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Example Question #79 : Proportions

Solve the proportion: $\frac{3x}{2x+1} = \frac{8}{3}$

Possible Answers:

$-\frac{8}{7}$

$-\frac{5}{3}$

$\textup{No solution.}$

$-\frac{1}{7}$

$-\frac{10}{13}$

Correct answer:

$-\frac{8}{7}$

Explanation:

Before we cross multiply, we have to make sure to note that there is an existent in the denominator. Recall that a denominator cannot be zero.

Set the denominator equal to zero and solve for .

2x+1=0

2x=-1

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

The final answer cannot be $x=-\frac{1}{2}$ after solving the proportion.

Cross multiply the fractions given.

3(3x)=8(2x+1)

Simplify by distribution.

9x=16x+8

Subtract on both sides and simplify.

9x-9x=16x+8-9x

0=7x+8

Subtract on both sides.

-8=7x

Divide by on both sides.

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

The answer is: $x=-\frac{8}{7}$

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Example Question #73 : Proportions

Solve the proportion: $\frac{3x}{7} = \frac{1}{14}$

Possible Answers:

$-\frac{97}{3}$

$\frac{1}{6}$

$-\frac{1}{6}$

$\frac{97}{3}$

Correct answer:

$\frac{1}{6}$

Explanation:

Cross multiply both fractions.

(3x)(14) = 7(1)

Simplify both sides.

42x=7

In order to isolate x, we will need to divide both sides by 42.

$\frac{42x}{42}=\frac{7}{42}$

Reduce both fractions on the left and right side.

The answer is: $x= \frac{1}{6}$

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Example Question #1204 : Algebra 1

Solve the proportion: $\frac{2}{7x} =\frac{4}{21}$

Possible Answers:

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{1}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

Cross multiply the terms.

2(21)=4(7x)

Simplify both sides.

42=28x

Divide both sides by 28.

$\frac{42}{28}=\frac{28x}{28}$

Simplify both fractions.

$\frac{42}{28} = \frac{7\times 2 \times 3}{7\times 2 \times 2}$

Cancel out the similar terms.

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

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1201 : Algebra 1

Example Question #1202 : Linear Equations

Example Question #1203 : Linear Equations

Example Question #1202 : Algebra 1

Example Question #76 : Proportions

Example Question #1203 : Algebra 1

Example Question #78 : Proportions

Example Question #79 : Proportions

Example Question #73 : Proportions

Example Question #1204 : Algebra 1

All Algebra 1 Resources

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