GoalTurn a story or a sentence into a linear equation with one unknown.
New words
linear equation · an equation where the unknown has power 1, like 2x + 3 = 11unknown · the number we want to find, written xconsecutive · one after another, like 24, 26, 28equals · is the same amount as
Explanation
To form an equation, call the unknown x and find the two quantities that are equal. Read the sentence slowly: “twice a number minus 15 equals 12” gives 2x − 15 = 12. Words like “is”, “equals” and “gives” show where the = sign goes. For consecutive even numbers, each is 2 more than the one before: x, x + 2, x + 4. For consecutive odd numbers it is the same, since they also differ by 2. In stories look for a fixed part and a part that depends on x, such as a taxi with a start fee of 6 LE and 4 LE for every kilometre: the fare is 4x + 6.
In words
Equation
a number plus 5 is −3
x + 5 = −3
twice a number minus 15 equals 12
2x − 15 = 12
three consecutive even numbers add up to 78
x + (x + 2) + (x + 4) = 78
Worked examples
Numbers. “A number plus 5 is −3” gives x + 5 = −3. “Twice a number minus 15 equals 12” gives 2x − 15 = 12.
Consecutive numbers. Three consecutive even numbers add up to 78. Call the first x. The others are x + 2 and x + 4. The equation is x + (x + 2) + (x + 4) = 78. (The answer is 24, 26, 28, as we will see later.)
Stories. A taxi charges 6 LE to start and 4 LE per km. The fare is 30 LE. For x km the fare is 4x + 6, so 4x + 6 = 30. A ribbon 72 cm long goes round a card whose length is 8 cm more than its width x. The perimeter gives 2(x + x + 8) = 72.
Class activity
Riddle makers. With a grown-up, think of a secret number, say 6. Make a riddle such as “three times my number plus 2 is 20” and write it as an equation. Swap riddles and write each other’s equation without solving it.
Practice
1
Write as an equation: “a number plus 7 is 2”.
x + 7 = 2.
2
Write as an equation: “three times a number minus 4 is 11”.
3x − 4 = 11.
3
Two consecutive whole numbers add up to 51. Write an equation.
x + (x + 1) = 51.
4
A ticket costs x LE. Four tickets and a snack of 10 LE cost 58 LE. Write an equation.
4x + 10 = 58.
5
Youssef writes three consecutive even numbers as x, x + 1, x + 2. What is wrong?
Even numbers differ by 2, so write x, x + 2, x + 4.
