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Pre-Algebra : Two-Step Equations

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #51 : Algebraic Equations

Solve for :

4x+3=7

Possible Answers:

Correct answer:

Explanation:

The goal is to isolate the variable to one side.

4x+3=7

Subtract from each side of the equation:

4x+3-3=7-3

4x=4

Divide each side by :

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

x=1

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Example Question #1 : Two Step Equations

Solve for :

$6x^{2}=216$

Possible Answers:

$\pm 9$

$\pm 3$

$\pm 6$

Correct answer:

$\pm 6$

Explanation:

The goal is to isolate the variable to one side.

$6x^{2}=216$

Divide each side by :

$\frac{6x^{2}}{6}=\frac{216}{6 }$

$x^{2}= 36$

Take the square root of each side:

$\sqrt{x^2}=\sqrt{36}$

$x=\pm 6$

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Example Question #2 : Two Step Equations

Solve for :

$3x^{^{3}}+4=28$

Possible Answers:

Correct answer:

Explanation:

The goal is to isolate the variable to one side.

$3x^{^{3}}+4=28$

Subtract from each side:

$3x^{^{3}}+4-4=28-4$

$3x^{^{3}}=24$

Divide each side by :

$\frac{3x^{^{3}}}{3}=\frac{24}{3}$

x^3=8

Take the cube root of each side:

$\sqrt[3]{x^3}=\sqrt[3]{8}$

x=2

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Example Question #4 : Two Step Equations With Integers

Solve for :

x^2+20=45

Possible Answers:

$\pm5$

$\pm15$

Correct answer:

$\pm5$

Explanation:

The goal is to isolate the variable to one side.

x^2+20=45

Subtract from each side:

x^2+20-20=45-20

x^2=25

Take the square root of each side:

$\sqrt{x^2}=\sqrt{25}$

$x=\pm5$

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Example Question #5 : Two Step Equations With Integers

Solve for .

2x+5=19

Possible Answers:

Correct answer:

Explanation:

Step 1: Subtract from both sides:

2x+5-5=19-5

2x+0=14

2x=14

Step 2: Divide both sides by :

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

x=7

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Example Question #5 : Two Step Equations With Integers

4x -3=33

Possible Answers:

Correct answer:

Explanation:

To solve two-step equations, first move everything that does not have the variable over to the other side of the equation. In order to move the -3 to the other side of the equation, you must do the opposite operation (addition). Keep in mind you must do the same step on each side of the equation every time you change something.

4x-3=33

+3=+3

The equation should now look like this:

4x=36

Next, isolate the variable by moving it to the other side of the equation. Do this by doing the opposite operation (division):

$\frac{4x}{4}=\frac{36}{4}=9$

The result should be the following:

x=9

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Example Question #1 : Two Step Equations With Integers

7x -2 =47

Possible Answers:

Correct answer:

Explanation:

To solve two-step equations, first move everything that does not have the variable over to the other side of the equation. In order to move the -2 to the other side of the equation, you must do the opposite operation (addition). Keep in mind you must do the same step on each side of the equation every time you change something.

7x-2=47

+2=+2

The equation should now look like this:

7x=49

Then, isolate the variable by moving the 7 to the other side of the equation. Do this by doing the opposite operation (division).

$\frac{7x}{7}=\frac{49}{7}=7$

The result should be the following:

x=7

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Example Question #2 : Two Step Equations With Integers

15x-38=82

Possible Answers:

Correct answer:

Explanation:

To solve two-step equations, first move everything that does not have the variable over to the other side of the equation. In order to move the -38 to the other side of the equation, you must do the opposite operation (addition). Keep in mind you must do the same step on each side of the equation every time you change something.

15x-38=82

+38=+38

The equation should now look like this:

15x=120

Then, isolate the variable by moving the 15 to the other side of the equation. Do this by doing the opposite operation (division).

$\frac{15x}{15}=\frac{120}{15}=8$

The result should be as follows:

x=8

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Example Question #6 : Two Step Equations With Integers

Solve for x:

2x+14=58

Possible Answers:

x=23

x=22

$\frac{x}{2}=\frac{54}{-14}$

2x=44

x=15

Correct answer:

x=22

Explanation:

In order to find x, you need to isolate it. If x isn't alone, you haven't finished solving the problem!

Step 1: subtract 14 from both sides of the equation

2x+14-14=58-14

2x=44

Step 2: divide both sides of the equation by 2

$\frac{2x}{2}=\frac{44}{2}$

x=22

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Example Question #7 : Two Step Equations With Integers

Solve for x:

-5x+4=-21

Possible Answers:

x=5

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

x=-5

x=-30

x=6

Correct answer:

x=5

Explanation:

Step 1: subtract 4 from both sides

-5x+4=-21

-5x+4-4=-21-4=-25

Step 2: divide both sides by -5 to isolate x

$\frac{-5x}{-5}=\frac{-25}{-5}$

Solve:

$x=\frac{-25}{-5}=5$

x=5

Remember, a negative integer divided by another negative integer will have a positive answer.

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Pre-Algebra : Two-Step Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #51 : Algebraic Equations

Example Question #1 : Two Step Equations

Example Question #2 : Two Step Equations

Example Question #4 : Two Step Equations With Integers

Example Question #5 : Two Step Equations With Integers

Example Question #5 : Two Step Equations With Integers

Example Question #1 : Two Step Equations With Integers

Example Question #2 : Two Step Equations With Integers

Example Question #6 : Two Step Equations With Integers

Example Question #7 : Two Step Equations With Integers

All Pre-Algebra Resources

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