Review: expressions, equations, inequalities and relationships
Discover Mathematics P6: Term 1, Units 1–7, Review
GoalRevise writing and evaluating expressions, solving one-step equations and inequalities, and linking two variables.
New words
expression · numbers, letters and operations, such as 3n + 8equation · a statement that two expressions are equalinequality · a statement using <, >, ≤ or ≥dependent variable · the quantity that changes because of the other one
Explanation
A letter stands for an amount that can change, so 3n means 3 times n. To evaluate an expression we substitute a number and follow the order of operations: brackets, powers, then × and ÷, then + and −. Two expressions are equivalent when they give the same value for every number, like 2(x + 4) and 2x + 8. To solve an equation we use the inverse operation on both sides and then check by substituting. An inequality has many solutions; on a number line an open circle means the number is not included and a filled circle means it is included. When one quantity depends on another, we call them the dependent and the independent variable, and we can show the link with a table, an equation or a graph.
★Remember
Substitute, then brackets → powers → × ÷ → + −. Solve with the inverse operation and check. Open circle: not included; filled circle: included.
Worked examples
ƒFormula
3n + 8
A notebook costs 8 LE and a pen costs 3 LE. The cost of one notebook and n pens is 3n + 8 LE. For n = 5 the cost is 3 × 5 + 8 = 15 + 8 = 23 LE. Also 2 + 3 × 4² = 2 + 3 × 16 = 2 + 48 = 50, because the power comes first, then the multiplication.
Solve x + 17 = 40: subtract 17 from both sides, x = 23. Check: 23 + 17 = 40. Solve 6x = 54: divide both sides by 6, x = 9. An inequality: a lift carries at most 8 people, so p ≤ 8. The number line below shows x ≥ 3, with a filled circle at 3: 3 is included, and so are 4, 5, 6 and every number to the right.
A bakery sells bread at 4 LE a loaf. The number of loaves n is the independent variable and the cost c is the dependent variable. The equation is c = 4n. The table gives the ordered pairs (1, 4), (2, 8), (3, 12), (4, 16), (5, 20). Seven loaves cost 4 × 7 = 28 LE.
Class activity
Rule maker. Choose a price for something small you like (for example a sweet or a notebook). Write the equation for the cost c of n of them, make a table for n = 1 to 5, and use it to find the cost of 12. Then write an inequality for how many you can buy with 50 LE.
Practice
1
Write an expression for “7 more than three times y” and evaluate it for y = 4.
