Equations & Inequalities

Year 9 Term 1

Term

A term consists of numbers and pronumerals combined with multiplication or division eg. 4x, -3y, -8

Pronumeral (variable

A pronumeral is a letter that stands for a number. eg. x, y

Coefficient

A coefficient is the number in front of a pronumeral. eg. 4, -3

Constant Term

The constant term is a term that is just a number by itself. There are no pronumerals. eg. -8, 4, -3

Expression

Do not need to find an answer and has no equal sign. eg. 2a + 2b

Equation

Need to find an answer and has an equal sign. eg. 5a + 4 = 12

Solving word problems

1. Read the problem and find out what the question is asking for.

2. Define a variable and write a statement such as: ‘Let x be the number of …’ . The variable is often what you have been asked to find.

3. Write an equation using your defined variable to show the relationship between the facts in the question.

4. Solve the equation.

5. Answer the question in words.

6. Check the solution makes sense.

Linear Inequalities

Basically an equal sign for an equation that is ≤, ≥, <, >

Reversing Inequalities

If we need to swap sides (to make some questions easier) so that the pronumeral is on the left of the inequality sign, then we have to reverse/ swapped the symbol.

The sign needs to be reversed/ swapped when both sides of the inequality are being divided or multiplied by a negative number.

Inequalities on number lines

Less/ greater than or equal to has a closed dot. Less / greater than has open dot.

Arrow is pointing the same direction as the inequality.

Pronumeral has to be labeled on the umber line (on the left)

Identifying formulas

The subject in formulas is the pronumeral that is by itself on one side of the equation. It is usually on the left hand side. eg. E = mc²

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