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

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #41 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if .

Possible Answers:

Correct answer:

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 subtracted so we must add the number,  , to each side of the equation 

Perform the math so our equation becomes .

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

Perform the math to find the answer 

The answer is .

Example Question #42 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if .

Possible Answers:

Correct answer:

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 subtracted so we must add the number,  , to each side of the equation 

Perform the math so our equation looks like 

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

Perform the math to find the answer .

Example Question #43 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if

Possible Answers:

Correct answer:

Explanation:

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

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

Remember when you distribute a negative that both of the numbers inside the parentheses are being multiplied by a negative number so they must flip signs.

Our problem now looks like 

Then we must get our variable, , by itself.

We must add the number, , to each side of the equation 

Perform the math so our equation looks like 

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

Solve the math to find the answer .

Example Question #44 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if

Possible Answers:

Correct answer:

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 the each side of the equation to have 

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 

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

Perform the math 

The answer is .

Example Question #45 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for where .

Possible Answers:

Correct answer:

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 

Perform the math so our equation looks like 

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

Perform the math to find the answer .

Example Question #46 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for where

Possible Answers:

Correct answer:

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 subtracted so we must add the number,  , to each side of the equation 

Perform the math so our equation looks like 

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

Perform the math to find the answer .

Example Question #47 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if

Possible Answers:

Correct answer:

Explanation:

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

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

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

Then we must get our variable, , by itself.

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

Perform the math so our equation looks like 

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

Solve the math to find the answer .

Example Question #48 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if

Possible Answers:

Correct answer:

Explanation:

To solve for  we must get all of the numbers on the other side of the equation as .

When solving a simple two-step equation we must remove the numbers that are interacting with  in this order: Addition/Subtraction, Multiplication/Division, Exponents.

To do this in a problem where  is being multiplied by a number, we must divide both sides of the equation by the number.

In this case the number is  so we divide each side of the equation by  to make it look like this 

Our simplified equation becomes

To solve an equation with  we must take the square root of each side of the equation to get  by itself.

Doing this makes our problem look like 

Then we perform the square root to get the answer 

Remember that  can also equal  so our answer will be both positive and negative.

The final answer looks like .

Example Question #49 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if

Possible Answers:

Correct answer:

Explanation:

To perform a two step algebra problem with addition and division 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 subtracted so we must add the number,  , to each side of the equation 

Perform the math so our equation looks like 

Then we multiply each side of the equation by the number that is under  to get  by itself 

Perform the math to find the answer .

Example Question #41 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if

Possible Answers:

Correct answer:

Explanation:

To perform a two-step algebra problem with addition and division 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 

Perform the math so our equation looks like 

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

Perform the math to find the answer .

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