Math

• Variable


  A symbol, generally a lowercase letter, used to represent an unknown quantity
• Common variables used in algebra


  • x
  • y
  • z
• Algebraic expression


  One or more terms separated by plus or minus symbols
• Term


  A single number, variable, or a number times one or more variables
• Coefficient


  The number that multiplies a variable or variables in a term
• Constant


  A number that is not a variable and has a fixed value
• Simplifying an algebraic expression using the distributive property


  1. Distribute the coefficient to each term inside the parentheses

  2. Combine like terms
• Like terms


  Terms with the exact same variable(s) and exponents
• The coefficients of like terms can be different, but the variable parts must be the same
• If the variable parts are not the same, the terms are not like terms
• If the exponents are not the same, the terms are not like terms
• Term


  A single number or a number that is multiplied by one or many variables and those variables can be raised to powers
• Algebraic expression


  A single term or a collection of terms separated by plus or minus signs
• Equation


  A statement that two algebraic expressions are equal, always includes the equality symbol
• For an equation to be true, the left and right side must be the same value
• Solving an equation


  Determine the value of the variable that makes the left and right side equal
• Checking if a value is a solution to an equation involves substituting that value and verifying the left and right sides are equal
• If the left and right sides are not equal when substituting a value, that value is not a solution to the equation
• The only value that makes the equation true is the solution to the equation
• and the right side are equal if we do then we know that that value is a solution for the equation
• Solving the equation


  1. Start with negative 8

  2. Plug in negative 8 for k

  3. 3 times (4 times negative 8 + 4) = negative 84

  4. Verify that negative 8 is a solution
• Trying other values for k


  1. Plug in 7 for k

  2. 3 times (4 times 7 + 4) does not equal negative 84, so 7 is not a solution

  3. Plug in 0 for k

  4. 3 times (4 times 0 + 4) does not equal negative 84, so 0 is not a solution
• Only k equals negative 8 is a solution to the equation
• Solving the equation n^2 = 8n


  1. Plug in negative 4 for n

  2. Negative 4 squared = 16, which does not equal 8 times negative 4

  3. Plug in 0 for n

  4. 0 squared = 0, which equals 8 times 0

  5. Plug in 8 for n

  6. 8 squared = 64, which equals 8 times 8
• Solving the equation (x - 6)/(4x - 5)/(4x) = 1/x


  1. Plug in negative 1 for x

  2. Simplify the left side, it does not equal 1/negative 1

  3. Plug in 15 for x

  4. Simplify the left side, it equals 1/15
• x = 15 is a solution to the equation (x - 6)/(4x - 5)/(4x) = 1/x
• Coefficient of x


  The number multiplying the variable x
• Solving a linear equation with one variable

  1. Isolate the variable

  2. Perform the same operation on both sides to maintain the solution
• Linear equation with one variable


  ax + b = c, where a cannot be 0
• If a = 1, the equation simplifies to x + b = c
• Addition property of equality


  • Allows adding/subtracting the same number to both sides without changing the solution
• Solving x - 7 = -12


  1. Add 7 to both sides to isolate x

  2. x = -5
• Solving x + 5 = 2

  1. Subtract 5 from both sides to isolate x

  2. x = -3
• Solving z - 9 = -10


  1. Add 9 to both sides to isolate z

  2. z = -1
• Reciprocal


  The number that when multiplied by a given number, results in 1
• A number times its reciprocal is always 1
• The multiplication property of equality allows multiplying/dividing both sides by the same non-zero number without changing the solution
• x equals 7


  Correct solution
• Isolating x


  1. 3x equals 9

  2. Divide both sides by 3

  3. x equals 3
• Reciprocal


  A number times its reciprocal is always 1