☰ Year plan · Mathematics

Equations and inequalities

Week 8 · Solving equations and exploring and solving inequalities · 3 lessons
1

Solving equations by keeping the balance

Discover Mathematics P6: Term 1, Unit 4, Lessons 1–3
GoalSolve one-step equations by doing the same thing to both sides, and check by substituting.
New words
equation · a statement with an equals sign: two sides with the same valuesolution · the value of the letter that makes the equation trueinverse operation · the operation that undoes another: + and −, × and ÷
Explanation

An equation is like a pan balance that is level: the two sides have the same value. To find the unknown, we must keep the balance, so whatever we do to one side we do to the other. In x + 8 = 17, the 8 is added to x, so we undo it by subtracting 8 from both sides: x = 17 − 8 = 9. In 3x = 9, x is multiplied by 3, so we divide both sides by 3: x = 3. In x − 5 = 12 we add 5 to both sides: x = 17. In x ÷ 4 = 6 we multiply both sides by 4: x = 24. At the end we check by putting the answer back: 9 + 8 = 17 is true.

EquationUndo withSolution
x + 8 = 17subtract 8x = 9
x − 5 = 12add 5x = 17
3x = 9divide by 3x = 3
x ÷ 4 = 6multiply by 4x = 24
Worked examples
x817
x + 8 = 17. On the left is x and an 8 weight, on the right 17. Take 8 away from both pans: x = 9. Check: 9 + 8 = 17.
xxx9
3x = 9. Three equal weights x balance 9. Divide both sides by 3: x = 3. Check: 3 × 3 = 9.
xxxx48
Hana buys 4 notebooks for 48 LE. If one costs x LE, then 4x = 48. Divide both sides by 4: x = 12. One notebook costs 12 LE. Check: 4 × 12 = 48.
Class activity

Mystery bag. Put some beans in a closed bag and add 6 beans next to it. Tell a friend the total is 15 beans. The friend writes the equation x + 6 = 15, solves it and then opens the bag to check. Make a new puzzle with a multiplication, such as 3 equal bags with 12 beans in all.

Practice
1
Solve x + 6 = 15.
2
Solve x − 7 = 20.
3
Solve 5x = 45.
4
Solve x ÷ 3 = 8.
5
Karim had some stickers, got 14 more and now has 50. Write an equation and solve it.