## Objective:

**To check solutions of equations and translate verbal phrases into algebraic expressions.**

## Vocabulary

**Equation**- formed when an*equal*sign is placed between two expressions; it has a right side and a left side.**Open Sentence**- an equation containing a*variable*.**Solution**- a number that satisfies an equation (a number that makes the equation true).**Checking**- substituting a number into an equation to*check*to see if it is a solution.**Inequality**- formed when an*inequality symbol*is placed between two expressions; it has a right side and a left side.

## Notes:

### Notation - Inequality Symbols

**<**-*is**l*ess than (the angle symbol looks like an '*L*').**≤**-*is*less than or equal to.**>**-*is*greater than (is more than).**≥**-*is*greater than or equal to.

*is*".

When translating between verbal phrases and algebraic expressions write the numbers, variables, and symbols in the order that you come across them when the problem reads "is less than", "is greater than", and "is more than".

Note: If the problem reads "less than", "greater than", or "more than" (without the word "

__") then__

*is**reverse*the order of the variable and the number and use addition or subtraction. Do

**NOT**use the inequality symbols.

Example: Four is less than a number translates to

*4 < n*, while four less than a number translates to

*n − 4*.

### Addition

- The
*sum*of 6 and a number. -->*6 + n* - Eight
*more than*a number. -->*n + 8* - A number
*increased by*10. -->*n + 10*

### Subtraction

- The
*difference*of 5 and a number. -->*5 − n* - Four
*less than*a number. -->*n − 4* - Seven
*minus*a number. -->*7 − n* - A number
*decreased by*2. -->*n − 2*

### Multiplication

- The
*product*of 9 and a number. -->*9n* - Ten
*times*a number. -->*10n* - One half
*of*a number. -->

### Division

- The
*quotient of*a number and 4. --> - Seven
*divided by*a number. -->