ALGEBRA BASICS

• Solving equations


  Finding a value of the variable that makes the equation true
• Solving equations


  1. Isolate the variable

  2. Use inverse operations
• Expressions cannot be solved, only equations can be solved
• Simplifying


  Obeying the indicated operations
• Simplifying is one-sided, solving is two-sided
• Order of operations


  • Groupings
  • Exponents
  • Multiplication/Division
  • Addition/Subtraction
• Solving an equation with one variable


  1. Identify the operation between the variable and the number (multiplication, subtraction, etc.)

  2. Perform the opposite operation to isolate the variable

  3. Simplify the equation if possible

  4. Solve for the variable
• Negative 5/2


  Multiplying the entire expression in parentheses
• Negative 5/2 times (9r - 7)


  Equals negative 50
• Solving the equation


  1. Move the negative 5/2 term to the other side by dividing

  2. Simplify the equation by cancelling the negative 5/2 terms

  3. Solve for r
• The final answer is the value of r
• Solving algebraic equations


  1. Move anything outside of grouping first

  2. Divide by negative fraction to cancel

  3. Subtract to isolate variable

  4. Divide to isolate variable

  5. Take cube root to isolate variable
• The formula 136 = 1/2 * 8 * (15 + b) can be used to find the length of the second base of a trapezoid with area 136 cm^2 and height 8 cm, where the first base is 15 cm
• Solving for variable in equation


  • Identify variable to isolate
  • Move multipliers/exponents to isolate variable
  • Use opposite operations to isolate variable
• Equation E = 1/2 mv^2


  • Used to find kinetic energy given mass and velocity
  • Solve for velocity (v)
• Solving for variable in equation

  1. Identify variable to isolate

  2. Move multipliers by using reciprocal

  3. Divide to isolate variable

  4. Take square root to isolate variable
• Solution for v is square root of 2E/m