Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #21 : How To Find Absolute Value

Solve the absolute value:  

Possible Answers:

Correct answer:

Explanation:

Compute the terms inside the absolute value first.

Any value inside the absolute value will be converted to a positive value.

Compute the square by order of operation.

Simplify this expression.

The answer is:  

Example Question #3262 : Algebra 1

Solve the absolute value:  

Possible Answers:

Correct answer:

Explanation:

Solve the terms inside the absolute value first.

Simplify the absolute values.

Add the numbers.

The answer is:  

Example Question #3263 : Algebra 1

Solve the absolute value:  

Possible Answers:

Correct answer:

Explanation:

Solve the terms inside the absolute value first.

A negative value inside the absolute value sign will be converted to a positive value.

Use order of operation to solve.

The answer is:  

Example Question #3261 : Algebra 1

Possible Answers:

Correct answer:

Explanation:

The symbol above represents the absolute value, which we find by simply determining the positive value of the number in question. If the number is positive, it remains positive, but if it is negative, we just drop the negative sign. Therefore, the absolute value of  is .

Example Question #1 : How To Graph An Inequality With A Number Line

Which line plot corresponds to the inequality below?

Possible Answers:

Question_1_incorrect_1

Question_1_correct

Question_1_incorrect_3

Question_1_incorrect_2

Correct answer:

Question_1_correct

Explanation:

A closed circle indicates "greater than or equal to" or "less than or equal to," while and open circle indicates "greater than" or "less than". We can tell from the inequality that our line plot will only have closed circles, as the only symbol is "greater than or equal to."

Subtract  from both sides.

Divide both sides by .

Our plot will show a closed circle on , and extend infinitvely in the positive direction.

 

Example Question #1 : How To Graph An Inequality With A Number Line

What inequality is represented by the number line?

Question_5

Possible Answers:

 

Correct answer:

 

Explanation:

An open circle indictes "less than" or "greater than," while a closed circle indicates "greater than or equal to" or "less than or equal to".

This number line includes values that are less than  or greater than or equal to . Note how has an open circle, while has a closed circle.

Example Question #3262 : Algebra 1

Divide:

The answer must be in standard form.

Possible Answers:

Correct answer:

Explanation:

Multiply both the numerator and the denominator by the conjugate of the denominator which is  which results in

The numerator after simplification give us 

The denominator is equal to 

Hence, the final answer in standard form =

Example Question #3262 : Algebra 1

Solve the expression using the given values below.

, ,

Possible Answers:

Correct answer:

Explanation:

, ,

We can simply plug in the values to each occurrence of the variables.

For :

Then

Then

Now we can solve.

Example Question #1 : How To Find The Number Of Integers Between Two Other Integers

What is the sum of the prime integers that satisfy the inequality  ?

Possible Answers:

Correct answer:

Explanation:

The prime integers beterrn 20 and 40 are 23, 29, 31, and 37. Their sum is 

.

Example Question #1 : How To Find The Number Of Integers Between Two Other Integers

What is the sum of all of the perfect squares and perfect cubes that satisfy the inequality ?

Possible Answers:

Correct answer:

Explanation:

There are four perfect squares between 10 and 50: 16, 25, 36, and 49. There is one perfect cube, 27, in this range. Add:

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