Algebraic expressions With example Problems and also Interactive Exercises

Use the following examples and also interactive exercises to learn about Writing Algebraic Expressions.

You are watching: The sum of x and 9

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Problem: Ms. Jensen likes to divide her class into groups of 2. Usage mathematical symbols to stand for all the students in she class.

Solution: Let g represent the variety of groups in Ms. Jensen"s class.

Then 2 · g, or 2g deserve to represent "g teams of 2 students".

In the trouble above, the change g represents the variety of groups in Ms. Jensen"s class. A variable is a symbol provided to stand for a number in an expression or an equation. The worth of this number can vary (change). Let"s watch at an instance in i m sorry we use a variable.

Example 1: Write each expression as a mathematics expression.

PhraseExpression
the sum of nine and eight9 + 8
the sum of nine and also a number x9 + x

The expression 9 + 8 represents a solitary number (17). This expression is a numerical expression, (also called an arithmetic expression). The expression 9 + x represents a value that deserve to change. If x is 2, climate the expression 9 + x has a value of 11. If x is 6, then the expression has actually a worth of 15. So 9 + x is an algebraic expression. In the next few examples, we will be working solely with algebraic expressions.

Example 2: Write each phrase as an algebraic expression.

PhraseExpression
nine boosted by a number x9 + x
fourteen diminished by a number p14 - p
seven much less than a number tt - 7
the product of 9 and also a number n· n or 9n
thirty-two divided by a number y32 ÷ y or
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In instance 2, every algebraic expression had one number, one operation and also one variable. Let"s look at at an instance in i m sorry the expression consists of an ext than one number and/or operation.

Example 3: Write each phrase as an algebraic expression utilizing the change n.

PhraseExpression
five an ext than double a number2n + 5
the product that a number and 66n
seven split by twice a number÷ 2n or
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three times a number lessened by 113n - 11

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Example 4: A little company has $1000 to distribution to the employees as a bonus. Exactly how much money will certainly each employee get?

Solution: Let e represent the number of employees in the company. The quantity of money every employee will gain is stood for by the adhering to algebraic expression:

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Example 5: An electrician dues $45 per hour and spends $20 a work on gasoline. Write an algebraic expression to stand for his income for one day.

Solution: Let x stand for the variety of hours the electrician functions in one day. The electrician"s earnings have the right to be stood for by the complying with algebraic expression:

Solution: 45x - 20

Summary: A variable is a symbol provided to stand for a number in one expression or one equation. The value of this number deserve to change. An algebraic expression is a mathematics expression that is composed of variables, numbers and also operations. The value of this expression can change.

Exercises

Directions: pick the algebraic expression that effectively represents the expression provided. Select your price by clicking its button. Feedback to her answer is provided in the results BOX. If you do a mistake, pick a different button.

1. Fifteen less than twice a number 
 15 - 2x2x + 152x - 15None the the above.

RESULTS BOX: 

2. Three times a number, raised by seventeen 
 3(a + 17)3a + 17(17 + 3)aNone that the above.

RESULTS BOX: 

3. The product the nine and also a number, diminished by six 
 9(m - 6)6(9 - m)9m - 6None of the above.

RESULTS BOX: 

4. Thirty split by seven times a number 
 30 + 7n
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30(7n)
None that the above.

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RESULTS BOX:
5. Jenny earns $30 a work working part time in ~ a supermarket. Create an algebraic expression to stand for the amount of money she will certainly earn in d days. 
 30d
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30 + d
None that the above
 
RESULTS BOX: