Year 8 Equations and Inequalities

Fundamental concepts, definitions, and problem-solving steps for Year 8 algebraic equations and inequalities.

According to the transcript, how is the equation for the number $k$ being doubled, then three being added with a result of $52$ written?

$$2k + 3 = 52$$

What is the equation for Akira working $n$ hours earning $\$12$ per hour for a total of $\$156$?

$$12n = 156$$

What is the name of the method used in Key Topic 7E for solving equations with brackets?

Rainbow Method

In the context of formulas and relationships, what is a 'pronumeral'?

A variable, which is a letter.

How is a 'formula' or 'rule' defined in Key Topic 7G?

An equation containing two or more variables.

What is the 'subject' of an equation?

A variable which is also known as a pronumeral which is a letter.

If Jane and Luke have a combined age of $60$ and Jane is twice as old as Luke, what are their ages?

Luke is $20$ and Jane is $40$.

What is one condition that requires reversing the inequality symbol when solving an inequality?

Multiplying or dividing both sides by a negative number.

Besides multiplying or dividing by a negative number, what other operation requires reversing the inequality symbol?

Swapping sides of the inequality.

According to the diagrams and definitions in 7J, what are the four ways to obtain an equivalent inequality?

1. Adding or subtracting an expression from both sides; 2. Multiplying or dividing both sides by any positive number; 3. Multiplying or dividing both sides by a negative number and reversing the inequality symbol; 4. Swapping sides and reversing the inequality symbol.

What is the form of simple quadratic expressions discussed in Key Topic 7F?

$x^2 = c$ where $c > 0$