Module 1 of 6 · MA4-EQU-C-01
Two-step equations
Solve linear equations involving up to two steps
01
An equation is a balanced scale
An equation says two things are equal. Whatever you do to one side you must do to the other, or the scale tips and the equation stops being true. That single rule is the whole topic.
02
Undo in reverse order
To build 2x + 5 you multiply by 2, then add 5. To take it apart you go backwards: subtract 5 first, then divide by 2. Undoing the multiply first is the single most common mistake in this test.
03
Pronumerals on both sides
When x appears on both sides, move the smaller x term across first so the x you keep stays positive. 2x + 3 = 4x becomes 3 = 2x when you subtract 2x from both sides.
04
Fractions and brackets
A fraction like x/3 means divide by 3, so undo it by multiplying both sides by 3. Brackets like 3(x + 4) are undone either by dividing both sides by 3 or by expanding with the distributive law.
The rules to know by heart
- Balance ruleDo the same operation to both sides.
- Inverse operations+ undoes −, × undoes ÷, and the reverse.
- OrderUndo addition/subtraction first, then multiplication/division.
- CheckSubstitute your answer back in — LHS must equal RHS.
See it work
Try it — you choose the move, the scale stays balanced
3x + 7 = 22
A worked example
Solve for x.
7x − 11 = 10Worked solution
- 7x − 11 = 10
Every line has its reason in brackets. In the test, that bracket is worth marks on its own — write it even when the number feels obvious.
Words for this module
Equation
A number sentence with an equals sign, saying two expressions have the same value.
Watch out: 3x + 1 is an expression. 3x + 1 = 10 is an equation — only equations can be solved.
Pronumeral
A letter that stands for a number, such as the x in 2x + 5 = 11.
Watch out: 2x means 2 × x. The multiplication sign is never written.
Equivalent equations
Equations with the same solution, made by doing the same thing to both sides.
Watch out: 2x + 5 = 11, 2x = 6 and x = 3 are all equivalent — each line of your working is a new equivalent equation.
Inverse operation
The operation that undoes another: + and −, × and ÷.
Distributive law
a(b + c) = ab + ac — multiply the outside number by every term inside the brackets.
Watch out: 3(x + 4) = 3x + 12, not 3x + 4. The 3 must reach both terms.
Equations with fractions
An equation where the pronumeral is divided, like x/3 + 2 = 7. Multiply both sides by the denominator to clear it.
Watch out: Multiply every term by the denominator, including the ones without a fraction.
ready?
Practise until you get five in a row.