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 #281 : Pre Algebra

Solve for  if .

Possible Answers:

Correct answer:

Explanation:

To solve for  we must move all of the constants to the other side of the equation of .

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

To do this in a problem where  is 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 new problem will look like this:

We then must solve the polynomial.

To solve an equation with , we must take the square root of each side of the equation to isolate .

Doing this makes our problem look like .

Then we take the square root of both sides to get the answer, .

Always remember that  can also equal , so our answer most include both the positive and negative number.

The final answer is  .

Example Question #31 : 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 added, so we must subtract this number,  , from each side of the equation:

Perform the math so  that our equation looks like  .

Then we divide each side of the equation by the constant attached to  to get  by itself:

The answer is then .

Example Question #32 : 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 through both of the numbers inside by multiplying to get .

Then we must get our variable, , by itself.

To do this add to each side of the equation:

Perform the math so that our equation looks like .

Then we divide each side of the equation by the constant attached to  to get  by itself:

Then the answer is .

Example Question #33 : 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 that 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 that our equation looks like .

Then we multiply each side of the equation by the constant under  to get  by itself:

Then the answer is .

Example Question #181 : Algebraic Equations

Solve for  if .

Possible Answers:

Correct answer:

Explanation:

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

To do this we put all of the variables on the right side of the equation by subtracting  from each side of the equation:

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

Perform the math to get .

Then add  to both sides of the equation:

Perform the math:

At this point we must divide each side of the equation by the constant attached to  to isolate :

Then the answer is .

Example Question #31 : 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 isolate .

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 that our equation looks like .

Then we divide each side of the equation by the constant attached to :

Perform the math to find the answer, .

Example Question #32 : 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 isolate .

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 that 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 #33 : 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.

First distribute the  outside of the parentheses through to both of the numbers inside by multiplying:

Then we must isolate .

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

Perform the math so that our equation looks like .

Then we divide each side of the equation by the number attached to :

Then the answer is .

Example Question #34 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if .

Possible Answers:

Correct answer:

Explanation:

Subtracting  from the left and right side of the equation:

When adding or subtracting variables, only add or subtract the constants in front of the variables.

Perform the math to get .

Then to get all of the integers to the left side, we will subtract  from the right and left side of the equation:

Perform the math to get .

At this point we must divide each side of the equation by the constant attached to :

Perform the math to find the answer, .

Example Question #35 : 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 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 .

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