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
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