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Algebra 1 : Linear Equations

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Example Questions

Example Question #781 : Linear Equations

Solve the following equation: $\frac{1}{3}x-\frac{3}{4} = \frac{3}{5}$

Possible Answers:

$\frac{17}{20}$

$\frac{7}{2}$

$\frac{24}{11}$

$\frac{61}{20}$

$\frac{81}{20}$

Correct answer:

$\frac{81}{20}$

Explanation:

Add three-fourths from both sides.

$\frac{1}{3}x-\frac{3}{4}+(\frac{3}{4}) = \frac{3}{5}+(\frac{3}{4})$

Simplify both sides.

$\frac{1}{3}x= \frac{3}{5}+\frac{3}{4}$

In order add fractions on the right side, the denominators must be the same. Convert the two fractions by their least common denominator.

$\frac{1}{3}x= \frac{3 \times 4}{5 \times 4}+\frac{3 \times 5}{4 \times 5}$

$\frac{1}{3}x= \frac{12}{20}+\frac{15}{20}$

Add the fractions.

$\frac{1}{3}x= \frac{27}{20}$

Multiply by three on both sides to isolate .

$\frac{1}{3}x\times 3= \frac{27}{20}\times 3$

$x=\frac{81}{20}$

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Example Question #782 : Linear Equations

Solve the following equation for

12x-33=3

Possible Answers:

x=6

x=12

x=3

x=-3

x=36

Correct answer:

x=3

Explanation:

12x-33=3

Add to both sides of the equation.

12x-33+33=3+33

12x=36

Divde both sides by .

$\frac{12x}{12}=\frac{36}{12 }$

x=3

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Example Question #251 : How To Solve Two Step Equations

Solve the following equation for .

-7x+7=21

Possible Answers:

x=7

x=-1

x=-2

x=2

x=3

Correct answer:

x=-2

Explanation:

-7x+7=21

Subtract from both sides of the equation.

-7x+7-7=21-7

-7x=14

Divide both sides by

$\frac{-7x}{-7}=\frac{14}{-7}$

x=-2

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Example Question #252 : How To Solve Two Step Equations

Solve the following equation: 3-7x = 1

Possible Answers:

$\frac{4}{7}$

$-\frac{2}{7}$

$\frac{2}{7}$

$\frac{3}{7}$

$-\frac{4}{7}$

Correct answer:

$\frac{2}{7}$

Explanation:

Add on both sides. This will prevent from dividing by a negative seven later.

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

Simplify both sides.

3= 1+7x

Subtract one on both sides.

2=7x

Divide by seven on both sides.

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

Simplify both sides.

The answer is:

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

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Example Question #253 : How To Solve Two Step Equations

Solve the following for x:

-x+12=-2

Possible Answers:

x=-14

x=14

x=10

x=-10

Correct answer:

x=14

Explanation:

To solve any two step equation, you must isolate x. To do this, you must move everything else to the other side of the equation. first, start by moving terms that are further away from x and the move terms/constants that are close to x. Thus, our first step would be to subtract 12 from both sides.

-x=-2-12

-x=-14

Then, you must divide both sides by negative 1.

$\frac{-x}{-1}=\frac{-14}{-1}$

x=14

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Example Question #254 : How To Solve Two Step Equations

Solve the equation: -6+6x=12

Possible Answers:

Correct answer:

Explanation:

We will need to solve for x. First add 6 on both sides.

-6+6x+ 6=12 +6

Simplify both sides.

6x=18

Divide by six on both sides.

$\frac{6x}{6}=\frac{18}{6}$

The answer is: x=3

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Example Question #255 : How To Solve Two Step Equations

Solve the following equation: 6-7x =0

Possible Answers:

$\frac{6}{7}$

$-\frac{6}{7}$

$-\frac{7}{6}$

$\frac{7}{6}$

Correct answer:

$\frac{6}{7}$

Explanation:

To solve for the unknown variable, we can either add on both sides or subtract 6 on both sides.

Let's add on both sides since this will prevent us from having to divide by negative seven on both sides in the later steps.

6-7x +7x=0+7x

Simplify both sides.

6=7x

Divide by seven on both sides.

$\frac{6}{7}=\frac{7x}{7}$

Simplify.

$x=\frac{6}{7}$

The answer is: $\frac{6}{7}$

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Example Question #256 : How To Solve Two Step Equations

Solve the following equation: 35x-1= -69

Possible Answers:

$\frac{68}{35}$

$-\frac{68}{35}$

Correct answer:

$-\frac{68}{35}$

Explanation:

Add one on both sides.

35x-1+1= -69+1

Simplify both sides.

35x= -68

Divide by 35 on both sides. The fraction is irreducible.

The answer is: $-\frac{68}{35}$

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Example Question #257 : How To Solve Two Step Equations

Solve the following equation: 0.1x -0.2=0.3

Possible Answers:

1.5

Correct answer:

Explanation:

Add 0.2 on both sides.

0.1x -0.2+0.2=0.3+0.2

Simplify both sides.

0.1x=0.5

Divide by 0.1 on both sides to isolate x.

$\frac{0.1x}{0.1}=\frac{0.5}{0.1}$

Simplify both sides.

The answer is: x=5

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Example Question #781 : Algebra 1

Solve for x:

x^2-3=0

Possible Answers:

$x=-\sqrt{3}$

x=2, -2

$x=\sqrt{3}$

$x=\sqrt{3}, -\sqrt{3}$

Correct answer:

$x=\sqrt{3}, -\sqrt{3}$

Explanation:

To solve for x, first we must isolate the x terms to one side:

x^2=3

Finally, we must take the square root of both sides to solve for x:

$x=\sqrt{3}, -\sqrt{3}$

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #781 : Linear Equations

Example Question #782 : Linear Equations

Example Question #251 : How To Solve Two Step Equations

Example Question #252 : How To Solve Two Step Equations

Example Question #253 : How To Solve Two Step Equations

Example Question #254 : How To Solve Two Step Equations

Example Question #255 : How To Solve Two Step Equations

Example Question #256 : How To Solve Two Step Equations

Example Question #257 : How To Solve Two Step Equations

Example Question #781 : Algebra 1

All Algebra 1 Resources

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