Linear equations

• What is an equation?


  An equation is a statement with an equal sign (=) showing two expressions are equal.
• What does solving an equation involve?


  Solving an equation involves finding the value for which the two expressions are equal.
• Can equations be true all the time?


  No, equations are not always true.
• What is an identity?


  An identity is an equation that is always true, regardless of the values of the variables.
• How can an identity be represented?


  An identity can be written with the sign ≡.
• Give an example of an identity.


  2x + 3x ≡ 5x is an identity.
• What is a number machine?


  • A way of showing rules using a flow diagram.
  • It illustrates the operations applied to a variable.
• How can the equation 3J - 6 = 9 be represented in a number machine?

  J → ×3 → -6 = 9 represents the operations applied to J.
• What does the number machine representation J → ×3 → -6 = 9 mean?


  It means J has been multiplied by 3, then 6 has been subtracted, resulting in 9.
• How do you solve equations using number machines?


  First write the equation as a number machine, then reverse each step.
• What is the balance method in solving equations?


  The balance method involves applying the same operation to both sides of the equation to keep it balanced.
• Solve the equation 3a + 8 = 26 using the balance method.


  Subtract 8 from each side to get 3a = 18, then divide by 3 to find a = 6.
• What is the first step to solve the equation 5(2c - 3) = 19?


  The first step is to expand the bracket to get 10c - 15 = 19.
• What do you do after expanding the bracket in the equation 5(2c - 3) = 19?


  After expanding, simplify the equation to get 10c - 15 = 19.
• How do you isolate c in the equation 10c - 15 = 19?


  Add 15 to both sides to get 10c = 34, then divide by 10 to find c = 3.4.
• What should you do when an equation includes fractions?

  Use inverse operations to keep the equation balanced.
• How do you solve the equation 35 + 9 = 7/4?


  Multiply both sides by 4 to eliminate the fraction, resulting in 35 + 9 = 28.
• What is the process to solve an equation with fractions?


  The process involves doing the opposite operations to each side to maintain balance.
• What are the key steps in solving equations with brackets?


  1. Expand the bracket.
  2. Simplify the equation.
  3. Use the balance method to isolate the variable.
• What is the BIDMAS rule?


  • BIDMAS stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction.
  • It is used to determine the order of operations in calculations.