High School Math : Solving Equations

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #11 : Equations

Solve the following equation. 

Possible Answers:

Correct answer:

Explanation:

To begin solving, we use the distributive property to simplify the left side. We get: . Then, adding 25 to both sides, we get: . Dividing by 5, we get that

Example Question #12 : Equations

Solve the equation for

Possible Answers:

No solution

Correct answer:

Explanation:

Since we have variables on both sides, we first subtract  from both sides.

This leaves us with .

Subtracting 2 from both sides, we get

Example Question #13 : Equations

Solve for

Possible Answers:

Correct answer:

Explanation:

First, use the distributive property to multiply out the left side:

Then, add  on both sides: 

Subtract 2 from both sides: 

Divide both sides by 10 to get , or

Example Question #14 : Equations

Solve the following equation for .

Possible Answers:

Correct answer:

Explanation:

The first step in solving this equation is to distribute the 2 through the parentheses. This gives us:

Next, we subtract 6 from both sides, in order to get the variable alone on one side of the equation:

Finally, we divide both sides by 2 to solve for :

Example Question #15 : Equations

Solve the following equation for :

Possible Answers:

Correct answer:

Explanation:

The first step in solving this equation is to combine the like terms. That is, move all of the terms with an  in it to one side of the equation, and all the terms without an  to the other side. Let's begin with moving the terms to the left side of the equation. We do this by subtracting  from each side:

Next, we combine the terms without an on the right side. We do this by subtracting 3 from both sides:

Finally, we divide both sides of the equation by 2 to solve for :

Example Question #11 : Solving Equations

Solve the following equation for :

Possible Answers:

Correct answer:

Explanation:

The first step to solve this equation is expand out the right-hand side of the equation by multiplying the 4 through the parentheses:

Next, we combine like terms. That is, we put all of the terms with an  on one side of the equation and all the terms without on the other. We'll start by subtracting  from both sides:

And now we'll move the non- terms to the right-hand side by subtracting 2 and 10 from both sides:

Combining these terms, this simplifies to:

Next, we divide both sides by 8:

Which gives:

Example Question #12 : Solving Equations

Solve the following equation for y:

Possible Answers:

Correct answer:

Explanation:

The first step in solving this equation it to subtract 3 from both sides, so that the term with  is alone on one side of the equals sign.

which simplifies to:

From here, we multiply both sides by 2:

This gives:

Example Question #21 : Equations

Solve the following equation for :

Possible Answers:

Correct answer:

Explanation:

The first step to solving this equation is to combine the terms with  in them on the left-hand side of the equation. This gives:

Next, we can subtract  from both sides of the equation:

Which simplifies to:

Then, we subtract 2 from both sides of the equation:

And to finish, we now divide both sides by 2:

Which simplifies to:

Example Question #21 : Basic Single Variable Algebra

Solve the following equation for :

Possible Answers:

Correct answer:

Explanation:

The first step in solving this equation is to distribute the 3 through the parentheses on the left-hand side of the equation:

Which gives:

Now, in order to get rid of the fraction, we can multiply the whole equation by 3:

We can now combine the like terms on the left-hand side, which gives:

Now, we subtract  from both sides:

Next, we subtract 18 from both sides:

Last, we divide both sides by 7 to solve for :

Which gives,

Example Question #211 : Algebra Ii

Solve the following equation for

Possible Answers:

Correct answer:

Explanation:

 

To begin, we add 2 on both sides. We get . Dividing by 6 we get

Learning Tools by Varsity Tutors