Math (MODULE 2)

• What is the first step to solve the equation \(3(2x - 4) = 30\)?


  Distribute the 3 to both terms inside the brackets.
• What does the equation \(6x - 12 = 30\) simplify to after adding 12 to both sides?


  It simplifies to \(6x = 18\).
• What is the solution for \(x\) in the equation \(6x = 18\)?


  x = 3
• How do you form and solve the inequality "Two more than treble my number is greater than 21"?


  • Form the inequality: \(3x + 2 > 21\)
  • Solve:
  • \(3x > 19\)
  • \(x > 6.33\)
• What is the solution for \(x\) in the equation \(x + 1 = 2\)?


  x = 1
• What is the solution for \(x\) in the equation \(x + 3 = 11\)?


  x = 8
• How do you solve the equation \(4x - 5 = 3x + 24\)?


  • Rearrange to isolate \(x\):
  • \(4x - 3x = 24 + 5\)
  • \(x = 19\)
• What is the method for solving inequalities with unknowns on both sides?


  • Use the same methods as equations.
  • Example: \(5(x - 4) = 3(x - 2)\)
  • Check the solution by substituting back.
• What is the result of checking the equation \(5(4) - 20 = 3(4) - 6\)?


  0 = 6
• What is the definition of equations and formulae?


  • Equations: Include numbers and can be solved.
  • Formulae: Express relationships in symbols.
• What is the process for rearranging formulae to make \(y\) the subject?


  • Use inverse operations.
  • Example:
  • From \(y = x + 2\) to \(y = x - 7\).
• What is the method for rearranging a two-step equation like \(4x - 3 = 9\)?


  • Rearrange to isolate \(x\):
  • \(4x = 12\)
  • \(x = 3\)
• How do you make \(x\) the subject in the formula \(y = 4x - 3\)?


  • Rearrange:
  • \(y + 3 = 4x\)
  • \(x = \frac{y + 3}{4}\)
• What are the steps for rearranging and solving equations?


  • The steps are the same for solving and rearranging.
  • Example values for \(x\) and \(y\):
  • \(x = 4, 12, 0, -1, -4\)
  • \(y = 2, 6, 0, -2, -6\)
• How do you find the gradient of the line from the equation \(2y = 4x + 9\)?


  • Rearrange to make \(y\) the subject:
  • \(y = 2x + 4.5\)
  • Gradient = 2
• What are the two methods for solving inequalities with unknowns?


  • Method 1: Make \(x\) positive first.
  • Method 2: Keep the negative \(x\).
  • Example: \(2 - 3x > 7\) leads to \(x < -\frac{5}{3}\).
• What happens to the inequality when you multiply or divide by a negative number?


  You need to reverse the inequality.
• What happens when the net is folded into a cube?

  Point X meets two specific points on the cube.
• What is the main question posed in the study material?

  Which two points does point X meet when the net is folded into a cube?