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High School Math : How to solve two-step equations with integers in pre-algebra

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Example Questions

Example Question #216 : Algebraic Equations

Solve for if

5x+32=97

Possible Answers:

x=15

x=13

x=11

x=15

Correct answer:

x=13

Explanation:

To perform a two-step algebra problem with addition and multiplication we must remove the numbers from so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being added so we must subtract the number, , from each side of the equation.

5x+32-32=97-32

Perform the math so our equation looks like 5x=65

Then we divide each side of the equation by the number that is in front of to get by itself

$\frac{5x}{5}=\frac{65}{5}$

Perform the math to find the answer

x=13

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Example Question #217 : Algebraic Equations

Solve for if

4(x+7)=28

Possible Answers:

x=2

x=0

x=1

x=4

Correct answer:

x=0

Explanation:

The problem above is a two-step algebra problem with distribution.

To solve you must first distribute the outside of the parentheses to both of the numbers inside the parentheses by multiplying.

Perform the multiplication with and each of the numbers inside the parentheses to get our new equation,

4x+28=28

Then we must get our variable, , by itself.

We must subtract the number, , from each side of the equation

4x+28-28=28-28

Perform the math so our equation looks like

4x=0

Then we divide each side of the equation by the number that is in front of to get by itself

$\frac{4x}{4}=\frac{0}{4}$

Solve to find the answer

x=0

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Example Question #218 : Algebraic Equations

Solve for if

x+20=3x-18

Possible Answers:

x=19

x=18

x=21

x=17

Correct answer:

x=19

Explanation:

When there are variables and numbers on each side of the equation, to solve we must mathematically move the variables onto one side and the numbers onto the other.

To do this we put all of the variables on the right side of the equal sign by subtracting from each side of the equation to have

x-x+20=3x-x-18

When adding or subtracting variables you only add or subtract the numbers in front of the variables. If there is no number the number value is .

Perform the math

20=2x-18

Then to get all of the integers to the left side we will add to both sides of the equation to have

20+18=2x-18+18

Perform the math.

38=2x

At this point we must divide each side of the equation by the number that is in front of to get by itself

$\frac{38}{2}=\frac{2x}{2}$

Perform the math to find the answer

x=19

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Example Question #61 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for :

4=3n+4

Possible Answers:

n=3

n=1

n=2

n=0

Correct answer:

n=0

Explanation:

4=3n+4

4-4=3n+4-4

0=3n

$\frac{0}{3}=\frac{3n}{3}$

0=n

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Example Question #62 : How To Solve Two Step Equations With Integers In Pre Algebra

32x-15=49

Solve for .

Possible Answers:

2048

1.0625

Correct answer:

Explanation:

32x-15=49

32x-15+15=49+15

32x=64

$\frac{32x}{32}=\frac{64}{32}$

$x=\frac{64}{32}$

x=2

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Example Question #61 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for when $\frac{x}{4}-25=5$

Possible Answers:

x=90

$x=\frac{30}{4}$

x=9

x=120

Correct answer:

x=120

Explanation:

To solve for , begin by adding to both sides of the equation:

$\frac{x}{4}-25+25=5+25$

$\frac{x}{4}=30$

Then multiply both sides by :

$\frac{x}{4}\cdot 4=30\cdot 4$

x=120

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Example Question #62 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for when 5x+32=72

Possible Answers:

x=9

x=14

x=8

x=4

Correct answer:

x=8

Explanation:

To solve for , begin by subtracting from both sides of the equation:

5x+32-32=72-32

5x=40

Then divide both sides by :

$\frac{5x}{5}=\frac{40}{5}$

x=8

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Example Question #63 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for when x+20=3x+42

Possible Answers:

x=14

x=-11

x=-64

x=16

Correct answer:

x=-11

Explanation:

When there are variables on both sides of the equation, it is easiest to move them to the same side. Move all variables to the left side of the equation by subtracting from each side:

x+20-3x=3x+42-3x

-2x+20=42

Then subtract from each side of the equation:

-2x+20-20=42-20

-2x=22

Then divide each side by :

$\frac{-2x}{-2}=\frac{22}{-2}$

x=-11

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Example Question #61 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for when 7x-17=32

Possible Answers:

x=7

x=343

x=79

x=14

Correct answer:

x=7

Explanation:

To solve for , begin by adding to both sides of the equation:

7x-17+17=32+17

7x=49

Then divide both sides of the equation by :

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

x=7

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Example Question #225 : Algebraic Equations

Solve for when x+18=7x-18

Possible Answers:

x=24

x=-7

x=18

x=6

Correct answer:

x=6

Explanation:

When there are variables on both sides of the equation, it is easiest to move them to the same side. Move all variables to the right side of the equation by subtracting from each side:

x-x+18=7x-x-18

18=6x-18

Then add to both sides of the equation:

18+18=6x-18+18

36=6x

Then divide each side of the equation by :

$\frac{36}{6}=\frac{6x}{6}$

x=6

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High School Math : How to solve two-step equations with integers in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #216 : Algebraic Equations

Example Question #217 : Algebraic Equations

Example Question #218 : Algebraic Equations

Example Question #61 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #62 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #61 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #62 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #63 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #61 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #225 : Algebraic Equations

All High School Math Resources

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