109
Multi-step equations
Textbook: Part 3, lesson 109, pp. 123–125
GoalMulti-step equations: find the order of operations and undo the last one first.
New words
multi-step equation · tarkibli tenglamalast operation · oxirgi amalorder of operations · amallar tartibiroot · ildiz
Explanation
An equation with several operations on one side is called multi-step. To solve it: 1) imagine a number in place of the unknown; 2) find the order of operations on the left (brackets, then multiplication and division, then addition and subtraction); 3) undo the last operation by using the inverse; 4) solve the simple equation obtained. Finally check the root.
Worked examples
4 × x + 9 = 57. The last operation is addition. 4 × x = 57 − 9 = 48; x = 48 : 4 = 12. Check: 4 × 12 + 9 = 57.
(y + 6) : 3 = 11. The last operation is division. y + 6 = 11 × 3 = 33; y = 33 − 6 = 27. Check: (27 + 6) : 3 = 11.
Class activity
“Steps of the order”: children write an equation on cards and mark with coloured pencils which operation is undone at each step (step 1 in red, step 2 in blue).
Practice
1
Solve the equation 4 × x + 9 = 57.
12
2
Solve the equation (y + 6) : 3 = 11.
27
3
Solve the equation 60 − x : 3 = 45.
45
4
Solve the equation 5 × (z − 3) = 35.
10
5
Aziza added 12 to a number she thought of, multiplied the sum by 5 and got 100. Which number did she think of?
8