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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 #273 : How To Solve Two Step Equations

Solve the following equation: 3x+6 = -50

Possible Answers:

$\frac{44}{3}$

$\frac{56}{3}$

$-\frac{56}{3}$

$-\frac{44}{3}$

Correct answer:

$-\frac{56}{3}$

Explanation:

To isolate the $\textup{x-variable}$ , first subtract on both sides.

3x+6 -6= -50-6

Simplify both sides.

3x=-56

Divide by three on both sides.

$x =-\frac{56}{3}$

This fraction is irreducible.

The answer is: $-\frac{56}{3}$

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Example Question #274 : How To Solve Two Step Equations

Solve the following equation: 2-x =-20

Possible Answers:

Correct answer:

Explanation:

To isolate the x-variable, add on both sides to move it to the right side and turn the sign into positive so that we won't have to divide by a negative one.

2-x+x =-20+x

Simplify both sides.

2=-20+x

Add twenty on both sides.

2+20=-20+x+20

This will eliminate the negative twenty on the right side.

The answer is: 22=x

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Example Question #281 : How To Solve Two Step Equations

Solve the equation: $\frac{1}{12}x +12 = 24$

Possible Answers:

$11\frac{11}{12}$

$12\frac{1}{12}$

144

Correct answer:

144

Explanation:

Subtract twelve from both sides.

$\frac{1}{12}x +12 -12= 24-12$

Simplify both sides.

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

Multiply by twelve on both sides to eliminate the fraction on the left side.

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

Simplify both sides.

The answer is: x=144

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Example Question #282 : How To Solve Two Step Equations

Solve the equation: -4x-9=27

Possible Answers:

$-\frac{9}{2}$

$\frac{9}{2}$

Correct answer:

Explanation:

Add nine on both sides to isolate the variable term.

-4x-9+9=27+9

Simplify both sides.

-4x=36

Divide by negative four on both sides.

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

Simplify both sides.

The answer is: x=-9

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Example Question #283 : How To Solve Two Step Equations

Solve the equation: -3x-13=23

Possible Answers:

$-\frac{10}{3}$

Correct answer:

Explanation:

Add thirteen on both sides.

-3x-13+13=23+13

Simplify both sides.

-3x = 36

Divide by negative three on both sides.

$\frac{-3x }{-3}= \frac{36}{-3}$

Simplify both sides.

x=-12

The answer is:

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Example Question #284 : How To Solve Two Step Equations

Solve the equation: $\frac{2}{7}x + \frac{3}{7} = 2$

Possible Answers:

$\frac{11}{2}$

$\frac{1}{22}$

$\frac{2}{11}$

$\frac{5}{7}$

$\frac{1}{14}$

Correct answer:

$\frac{11}{2}$

Explanation:

Multiply the entire equation by seven to eliminate the fractions.

$7(\frac{2}{7}x + \frac{3}{7} = 2)$

The result is: 2x+3=14

Subtract three from both sides.

2x+3-3=14-3

Simplify both sides.

2x=11

Divide by two on both sides to isolate the variable.

The answer is: $x= \frac{11}{2}$

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Example Question #282 : How To Solve Two Step Equations

Solve the equation: 4x+7=-13

Possible Answers:

$-\frac{2}{3}$

$-\frac{3}{2}$

$-\frac{19}{4}$

Correct answer:

Explanation:

Subtract seven from both sides.

4x+7-7=-13-7

Simplify both sides of the equation.

4x=-20

Divide by four on both sides.

$\frac{4x}{4}=\frac{-20}{4}$

Simplify both fractions.

The answer is: x=-5

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Example Question #286 : How To Solve Two Step Equations

Solve the equation: -3x+7=-20

Possible Answers:

$\frac{13}{3}$

$-\frac{13}{3}$

$-\frac{21}{20}$

Correct answer:

Explanation:

Solve by first subtracting seven on both sides.

-3x+7-7=-20-7

-3x=-27

Divide by negative three on both sides.

$\frac{-3x}{-3}=\frac{-27}{-3}$

Simplify both sides of the equation.

The answer is: x=9

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Example Question #287 : How To Solve Two Step Equations

Solve the equation: -6x+9 = -54

Possible Answers:

$-\frac{43}{6}$

$-\frac{15}{2}$

$\frac{21}{2}$

$\frac{41}{2}$

Correct answer:

$\frac{21}{2}$

Explanation:

Subtract nine from both sides of the equation.

-6x+9 -9= -54-9

Simplify both sides.

-6x = -63

Divide by negative six on both sides.

$\frac{-6x}{-6} = \frac{-63}{-6}$

$x=\frac{63}{6}$

Reduce this fraction. Use common factors to reduce. Both the numerator and denominator are divisible by three.

$x=\frac{63}{6}=\frac{3\times 21}{3 \times 2}$

Cancel the threes.

The answer is: $\frac{21}{2}$

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Example Question #288 : How To Solve Two Step Equations

Solve the equation: -7x+40=61

Possible Answers:

$\frac{1}{3}$

$-\frac{101}{7}$

$-\frac{1}{3}$

Correct answer:

Explanation:

Subtract forty from both sides of the equation.

-7x+40-40=61-40

Simplify both sides of the equation.

-7x=21

Divide by negative seven on both sides of the equation.

$\frac{-7x}{-7}=\frac{21}{-7}$

Simplify both sides.

x=-3

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 #273 : How To Solve Two Step Equations

Example Question #274 : How To Solve Two Step Equations

Example Question #281 : How To Solve Two Step Equations

Example Question #282 : How To Solve Two Step Equations

Example Question #283 : How To Solve Two Step Equations

Example Question #284 : How To Solve Two Step Equations

Example Question #282 : How To Solve Two Step Equations

Example Question #286 : How To Solve Two Step Equations

Example Question #287 : How To Solve Two Step Equations

Example Question #288 : How To Solve Two Step Equations

All Algebra 1 Resources

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