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 less 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.
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 "is") then 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. -->
