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Letters for unknowns: expressions, equations, inequalities and formulas
Mathematics Prep 1 Term 1, Unit 2, Lesson 1
GoalWrite situations with a letter and tell an expression, an equation, an inequality and a formula apart.
New words
variable · a letter that stands for an unknown numberexpression · numbers and letters with operations, no = signequation · two expressions joined by an = signformula · a rule written with letters, like A = l × w
Explanation
A variable is a letter, such as x, that stands for an unknown number. We leave out the multiplication sign: 2x means 2 × x and lw means l × w. Words turn into expressions: “5 subtracted from 3 times a number” is 3x − 5, and “double a number plus 5” is 2x + 5. Look for the sign to tell the kinds apart: an expression has no = or < sign, an equation has =, an inequality has <, >, ≤ or ≥, and a formula is a rule with letters that you can use again and again, such as A = l × w. Watch the order: “5 subtracted from 3x” is 3x − 5, not 5 − 3x.
| Kind | Example | How to tell |
|---|---|---|
| expression | 3x − 5 | no =, <, > sign |
| equation | 3x − 5 = 7 | has = |
| inequality | 3x − 5 < 7 | has <, >, ≤ or ≥ |
| formula | A = l × w | a rule with letters |
Worked examples
Words to expressions. “7 more than 4 times a number” is 4x + 7. “Half of a number minus 3” is x/2 − 3. Five tickets at x LE and three snacks at y LE, with 20 LE off, cost 5x + 3y − 20 LE.
Which kind? 2x + 3 is an expression. 2x + 3 = 11 is an equation. 2x + 3 < 11 is an inequality. P = 4a (perimeter of a square) is a formula.
Using a formula. The volume of a cube is V = a³. For a side of 3 cm: V = 3 × 3 × 3 = 27 cm³. The area of a rectangle 7 cm by 4 cm is A = lw = 7 × 4 = 28 cm².
Class activity
Number machine. With a grown-up, pick a rule such as “double the number, then add 3”. Write it with x. Use it on five numbers and make a table. Then swap and guess each other’s rule from the table.
Practice
1
Write “6 more than twice a number” as an expression.
2x + 6.
2
Write “a third of a number minus 2” as an expression.
x/3 − 2.
3
A ticket costs 12 LE. Write the cost of n tickets and find the cost of 5 tickets.
Cost = 12n LE. For n = 5: 12 × 5 = 60 LE.
4
Say which is an expression, an equation or an inequality: 5x − 2, 5x − 2 = 13, 5x − 2 > 13.
5x − 2 is an expression; 5x − 2 = 13 is an equation; 5x − 2 > 13 is an inequality.
5
Youssef writes “5 subtracted from 3x” as 5 − 3x. What is wrong?
The 5 is taken away from 3x, so it is 3x − 5.