Common Core: High School - Algebra : Solving an Equation Step-by-Step: CCSS.Math.Content.HSA-REI.A.1

Study concepts, example questions & explanations for Common Core: High School - Algebra

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Example Question #1 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for , first combine like terms.

On the left-hand side of the equation there are two terms that contain . Therefore, add  and  together.

Now, move the  term from the left-hand side to the right-hand side. To accomplish this, subtract  from both sides.

   

                  

_____________________

               

Next, to isolate , subtract the constant from the right-hand side of the equation to the left-hand side.

    

   

______________

Example Question #2 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for , first combine like terms.

On the left-hand side of the equation there are two terms that contain . Therefore, subtract  from .

Now, move the  term from the left-hand side to the right-hand side. To accomplish this, subtract  from both sides.

   

                    

_____________________

           

Next, subtract the constant from the right-hand side of the equation to the left-hand side.

    

   

______________

Finally divide each side by three to solve for .

Example Question #3 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for , first combine like terms.

On the left-hand side of the equation there are two terms that contain . Therefore, add  and  together.

Now, move the  term from the left-hand side to the right-hand side. To accomplish this, subtract  from both sides.

   

                  

_____________________

               

Next, to isolate , subtract the constant from the right-hand side of the equation to the left-hand side.

    

    

______________

Example Question #4 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for , first combine like terms.

On the left-hand side of the equation there are two terms that contain . Therefore, add  and  together.

Now, move the  term from the left-hand side to the right-hand side. To accomplish this, subtract  from both sides.

   

                     

_____________________

               

Next, to isolate , subtract the constant from the right-hand side of the equation to the left-hand side.

    

    

______________

Example Question #5 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for , first combine like terms.

On the left-hand side of the equation there are two terms that contain . Therefore, add  and  together.

Now, move the  term from the left-hand side to the right-hand side. To accomplish this, subtract  from both sides.

   

                     

_____________________

               

Next, to isolate , subtract the constant from the right-hand side of the equation to the left-hand side.

    

    

______________

Example Question #1 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for , first combine the like terms on the left-hand side of the equation.

Therefore, the equation becomes,

Now, move all the variables to the right-hand side of the equation by adding  to both sides.

         

____________________

From here, subtract the constant on the right-hand side from both sides of the equation.

    

              

_______________

 

Lastly, divide by three on both sides of the equation to solve for .

Example Question #7 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for , first combine like terms by subtracting  from both sides.

 

           

__________________

Now, combine the constant terms. Add two to both sides of the equation.

          

______________

From here, divide by four to solve for .

Example Question #8 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for , first subtract one from both sides to combine the constant terms.

        

____________

From here, multiply by two on both sides to solve for .

The two in the numerator cancels the two in the denominator on the left-hand side of the equation; thus, isolating .

Example Question #9 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve for  first combine the constant terms by adding two to both sides of the equation.

       

_____________

From here, multiply each side of the equation by 3 to solve for .

The three in the numerator cancels out the three in the denominator on the left-hand side of the equation; thus, solving for .

Example Question #2 : Solving An Equation Step By Step: Ccss.Math.Content.Hsa Rei.A.1

Solve for .

Possible Answers:

Correct answer:

Explanation:

First, combine like terms on both sides of the equation.

On the left-hand side:

Thus the equation becomes,

Now, subtract  from both sides.

      

             

__________________

Lastly, divide by negative one on both sides.

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