## Algebraic Expressions

Let"s obtain down to business. An expression is made up of terms.**Terms**space the separate values in one expression. Every term have the right to be a variable, a number and also a variable, or a number and also many variables v or without exponents, as lengthy as whatever is gift multiplied with each other in a single nugget of math goodness. Some of our favorite terms include:

77*x*7*x*2*y**x*6*y*11*z*2

These every count as a solitary term.

You are watching: Three less than twice a number

A number beside a variable method that number and also variable space being multiplied. The same is true for two variables next to each other: it way they"re gift multiplied. Due to the fact that the × we offered for multiplication in the previous looks an terrible lot choose the variable *x*, we"ll protect against using a symbol because that multiplication at all. Some speak to it lazy; we call it efficient.

Some terms are numbers only. These are called **constants**, or numbers that don"t change. Others have **variables** (letters that stand for an unknown or an altering number), and also some have variables and also numbers mashed together, in which case the number are referred to as **coefficients**.

Occasionally terms, favor the critical one above, seem come be missing a coefficient. Here"s the thing: they actually do have actually a coefficient of 1. It"s simply too lazy to display up. Since 1 times anything is just that anything, we typically don"t compose 1 as a coefficient, but it"s constantly there.

Example: *x* is the exact same thing together 1*x*, and *x*3*y*2*m* is the same thing together 1*x*3*y*2*m*.

**Variable**: one unknown or changing number. Often represented through *x*.**Constant**: a number the doesn"t change.**Coefficient**: the number that"s multiply by the variable.

We choose terms, and also we especially like *like* terms. **Like terms** space terms that have the exact same variables, including the exponents the go with those variables. The variables can be in different orders and also have different coefficients, however they all must be there.

**Examples:**3*xy* and -5*xy* **are** like terms (same variables).3*xy* and also -5*xym* **are not** favor terms (the second term has actually a variable the the an initial doesn"t).

-2*m*2*xh* and 4*m*2*hx* **are** prefer terms (same variables and exponents, simply in different order).-2*m*3*xh* and 4*m*2*xh* **are not** choose terms (the change *m* has different exponents in every term).

If there"s more than one hatchet separated by plus or minus signs, then we have actually an **expression**. For example:

5*x*2*y* – 3*xy* + *y* + 5

This expression has 4 terms: 5*x*2*y*, -3*xy*, *y* (or 1*y*), and 5.

### Names because that algebraic expressions

monomial | 1 Term | xy |

binomial | 2 Terms | xy – 2x |

trinomial | 3 Terms | xy – 2x + 3y |

quadnomial | 4 Terms | xy – 2x + 3y – 1 |

Here is a chart of typical phrases.

Common Words and also Phrases for:AddSubtractMultiplyDivideEqualsplusaddsummore thanin enhancement togreater thantotal and also | differencesubtractless thantake far | productoftimestwice (×2)factor | divided byquotientsplitsharedistribute | is |

In this translations, we"ll usage the letter *x* to represent the variable, though any type of letter, symbol, or emoticon would work. Smiley faces and also hearts, anyone?

a number enhanced by twelve | x + 12 |

the amount of double a number and also six | 2x + 6 |

eighty less than a number | x – 80 |

twenty-eight separation in half | 28 ÷ 2 |

the product that a number and also seven | 7x |

the quotient that a number and also four | x ÷ 4 |

five better than three times a number | 3x + 5 |

a number distributed evenly amongst six | x ÷ 6 |

the complete of forty and also a number | 40 + x |

three times the full of a number and five | 3(x + 5) |

A number is an unfavorable ten. | x = -10 |

A number plus 2 is eight. | x + 2 = 8 |

The difference between a number and seven is negative three. | x – 7 = -3 |

One less than double a number is seventeen. | 2x – 1 = 17 |

Twelve is the product of a number and three. | 12 = 3x |

Half the a number is twenty. See more: What Is The Gcf Of 12 And 30 Gcf(12,30), Gcf Of 12 And 30 | ½x = 20 |

A number is same to the sum of twice the number and an adverse three. | x = 2x + (-3) |

**Look Out:** be really careful through "less than." Three much less than a number is analyzed as "*x* – 3." The turning back of that, "3 – *x*," would certainly be a number less than 3.