Page 96 - Knowledge Organiser Yr8 24-25

Knowledge Base: Mathematics TOPIC 15: Solving Equations Year 8 | Autumn Term 2
By the end of this topic you should be able to:
• Solve one step equations
• Solve multi-step equations
• Solve equations with brackets
• Solve equations with unknowns on both sides
• Solve equations with fractions
• Solve equations using trial and improvement
Language
Meaning
Example
Expression
Made from numbers, letters and operations, but not including an equals sign
2a + 3b
Term
Part of an expression between plus or minus signs
In the example above, 2a and 3b are terms
Unknown
The letter in the equation that you are trying to find the value of
In the equation 6x – 2 = 28, x is the unknown
Equation
An expression equal to a number or another expression
x + 3 = 11
2x – 6 = x + 3
Solve
To find the value of an unknown in an equation that makes it true
If x + 5 = 12 Then x = 11
Solution
The value(s) of the unknown that the equation is true for
x = 11 is the solution
Inverse
An operation that reverses the effect of a given operation
The inverse of + 5 is-5 The inverse of ×3 is ÷3
Expand
To multiply out all brackets and then collect like terms
Expanding 2(3x + 5) – 7 + 4x gives 6x + 3
Substitution
A method for checking if your solution to an equation is correct by replacing the unknown with the solution
Substituting x = 3 into 2x + 1 gives 2 × (3) + 1 = 7
Trial and Improvement
A method for solving complex equations by making a guess, then improving on that guess until you are very close to the correct answer
The equation x2 + x = 245 can be solved by trial and improvement
Important things to remember:
Whatever you do to one side of the equation you do to the other!
The inverse of + is – The inverse of × is ÷
The inverse of 2 (square) is √ (square root)
Worked examples
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