High School Math : Basic Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #21 : 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 #22 : 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 #23 : 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 #24 : Equations

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 #25 : Equations

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

Example Question #26 : Equations

Solve:

Possible Answers:

Correct answer:

Explanation:

Add the two equations together to get . Then divide by to get .

Now substitute this value into one of the original equations to get

Next subtract from both sides to get .

Now divide both sides by to get .

Therefore the answer is .

Example Question #27 : Equations

Lilac paint is made by mixing one part blue paint and one part red pain with two parts white paint.  How many gallons of white paint should be mixed with two quarts of blue paint?

Possible Answers:

Correct answer:

Explanation:

Set up a proportion where number of quarts of white paint.

and solve by cross multiplying to get , and .

Example Question #28 : Equations

What number is of ?

Possible Answers:

Correct answer:

Explanation:

For percentage problems look for verbal cues:

"IS" means equals.

"OF" means multiplication.

Therefore the equation becomes .

Example Question #29 : Equations

An art show wants to focus on sculpture but will also accept paintings and drawings.  The show has room for pieces and will display them in a ratio of scupltures to painting to drawings.  How many sculptures will be displayed?

Possible Answers:

Correct answer:

Explanation:

Since the paintings and the drawings have the same ratio, they will have the same number on display.

Let number of paintings displayed = number of drawings displayed.

Then, number of sculptures displayed.

Set up a proportion:

Solve by cross multiplying to get or .

Then add to both sides to get .

Then divide by to get .

So there are drawings and paintings in the show, leaving the last spots for sculptures.

 

Example Question #30 : Equations

What number is of ?

Possible Answers:

Correct answer:

Explanation:

Verbal cues include "IS" means equal and "OF" means multiplication.

So the equation to solve becomes

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