Chapter 10: Linear Equations

Linear Equations

• To solve a linear equation you need to get the letter on its own on one side
• It is really important to write your working neatly when you are solving equations
    * 5x + 3 = 18
    * -3
    * 5x = 15
    * /5
    * x=3
      * Every line of working should have an equals sign in it
      * Start a new line for each step, do one operation at a time
      * Write down the operation you are carrying out, remember to do the same thing to both sides of the equation
      * Line up the equals signs

Letter on both sides

• To solve an equation you have to get the letter on its own on one side of the equations
• Start by collecting like terms so that all the letters are together
    * 2 - 2x = 26 + 4x
    * +2x
    * 2 = 26 + 6x
    * -26
    * -24 = 6x
    * /6
    * -4 = x

Equations with brackets

• Always start by multiplying out the brackets then collecting like terms
    * 19 = 8 - 2(5 - 3y)
    * 19 = 8 - 10 + 6y
    * +2
    * 21 = 6y
    * 21/6 = y

Examiners report

• Don’t use a trial and improvement method to solve an equation
• You probably won’t find the correct answer, and you can’t get any method marks

Equations with fractions

• When you have an equation with fractions, you need to get rid of any fractions before solving
• You can do this by multiplying every term by the lowest common multiple of the denominators
• x/3 + x+1/5 = 11
• x15
• 5x + 3x-3 = 165
• +3
• 8x = 168
• /8
• x = 21

Multiplying by an expression

• You might have to multiply by an expression to get rid of the fractions
• 20/n-3 = -5
• xn-3
• 20 = -5(n-3)

Worked practice

• Eliminate fractions before you start solving the equation
• You can do this by multiplying both sides of the equation by 4
• Use brackets to show that you are multiplying everything by 4
• Multiply out the brackets, then solve the equation normally
• Remember that your answer could be a fraction