15
Simplifying expressions
Textbook: Part 1, lesson 15, pp. 60–63
GoalUse the rules for opening brackets and taking out a common factor to simplify expressions; solve equations.
New words
simplifying an expression · ifodani soddalashtirishopening brackets · qavslarni ochishcommon factor · umumiy ko‘paytuvchiequation · tenglama
Explanation
Reading the distributive law from left to right gives the rule for opening brackets: 4(x + 3) = 4x + 12. Reading it from right to left gives the rule for taking a common factor out of brackets: 6x + 3x = (6 + 3)x = 9x. These rules are used to shorten expressions and make calculation easier. After simplifying, equations are easier to solve: from 6x + 5x + 13 = 57 we get 11x + 13 = 57, then 11x = 44 and x = 4. The grouping property is also used in simplifying: 3x · 4 · 5 = 60x.
Worked examples
6(x + 4) = 6x + 24; 27 × 13 + 73 × 13 = (27 + 73) × 13 = 100 × 13 = 1 300; 4a + 9 + 3a + 1 = 7a + 10.
5x + 4x + 12 = 66 → 9x + 12 = 66 → 9x = 54 → x = 6. Check: 5 × 6 + 4 × 6 + 12 = 30 + 24 + 12 = 66.
Class activity
“Simplifying relay”: teams simplify the expression on a card (for example 7a + 5 + 2a + 8) one step at a time; the first team to finish wins.
Practice
1
Open the brackets in 7(x + 5).
7x + 35
2
Take out the common factor and compute 38 × 9 + 62 × 9.
900
3
Solve 6x + 3x + 17 = 80.
7
4
Why is 4x + 3x = 7x?
x is a common factor: 4x + 3x = (4 + 3)x = 7x; four x's and three more x's make seven x's.