## Algebraic Expressions With Example Problems and Interactive Exercises

Use the complying with examples and also interenergetic exercises to learn about Writing Algebraic Expressions.

You are watching: Seven less than twice a number equals 19

Solution: Let g represent the number of groups in Ms. Jensen"s course.

Then 2 **·** g, or 2g have the right to represent "g teams of 2 students".

In the difficulty above, the variable g represents the number of groups in Ms. Jensen"s course. A **variable** is a symbol supplied to represent a number in an expression or an equation. The worth of this number have the right to differ (change). Let"s look at an example in which we usage a variable.

Example 1: Write each expression as a mathematical expression.

Phrase | Expression |

the amount of nine and eight | 9 + 8 |

the amount of nine and also a number x | 9 + x |

The expression **9 + 8** represents a single number (17). This expression is a numerical expression, (likewise referred to as an arithmetic expression). The expression **9 + x** represents a value that deserve to adjust. If x is 2, then the expression **9 + x** has actually a worth of 11. If x is 6, then the expression has a worth of 15. So **9 + x** is an algebraic expression. In the following few examples, we will certainly be functioning exclusively via algebraic expressions.

Example 2: Write each phrase as an algebraic expression.

Phrase | Expression |

nine increased by a number x | 9 + x |

fourteenager lessened by a number p | 14 - p |

salso less than a number t | t - 7 |

the product of 9 and also a number n | 9 · n or 9n |

thirty-2 split by a number y | 32 ÷ y or |

In Example 2, each algebraic expression consisted of one number, one procedure and one variable. Let"s look at an example in which the expression consists of more than one number and/or operation.

Example 3: Write each phrase as an algebraic expression using the variable n.

Phrase | Expression |

five even more than twice a number | 2n + 5 |

the product of a number and 6 | 6n |

salso separated by twice a number | 7 ÷ 2n or |

three times a number diminished by 11 | 3n - 11 |

Solution: Let e recurrent the number of employees in the agency. The amount of money each employee will obtain is stood for by the following algebraic expression:

Example 5: An electrician charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression to recurrent his revenue for someday.Solution: Let x represent the number of hours the electrician works in at some point. The electrician"s revenue deserve to be stood for by the adhering to algebraic expression:

Solution: 45x - 20

Summary: A **variable** is a symbol supplied to reexisting a number in an expression or an equation. The value of this number have the right to change. An **algebraic expression** is a mathematical expression that is composed of variables, numbers and operations. The worth of this expression have the right to adjust.

**Exercises**

Directions: Choose the algebraic expression that properly represents the phrase provided. Select your answer by clicking its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, choose a various switch.

1. | Fifteenager less than twice a number |

15 - 2x2x + 152x - 15Namong the over. RESULTS BOX: |

2. | Three times a number, boosted by seventeen |

3(a + 17)3a + 17(17 + 3)aNone of the over. RESULTS BOX: |

3. | The product of nine and also a number, lessened by six |

9(m - 6)6(9 - m)9m - 6None of the above. RESULTS BOX: |

4. | Thirty divided by seven times a number | |

30 + 7n | ||

30(7n) | ||

Namong the above. See more: What Is The Electron Configuration For Arsenic ? Arsenic » Properties Of Free Atoms |

RESULTS BOX: |

5. | Jenny earns $30 a day functioning component time at a supersector. Write an algebraic expression to reexisting the amount of money she will earn in d days. | |

30d | ||

30 + d | ||

None of the above |

RESULTS BOX: |