110
Simplifying equations
Textbook: Part 3, lesson 110, pp. 126
GoalSimplifying equations: calculate the numerical expression first, then solve.
New words
simplifying · soddalashtirishnumerical expression · sonli ifodareduce to · tenglamaga keltirishequation for a word problem · masalaga doir tenglama
Explanation
If one side of an equation contains only numbers, we first calculate that numerical expression by the order of operations, which simplifies the equation. For example in x + 25 = 9 × 6 − 17 the right side is 54 − 17 = 37, so x + 25 = 37, a simple equation. For word problems we also form an equation: denote the unknown by a letter, write the operations of the story one after another, then solve and check.
Worked examples
y − 15 = 7 × 8 − 20 → y − 15 = 36 → y = 36 + 15 = 51. Check: 51 − 15 = 36 and 56 − 20 = 36.
We multiplied x by 6, added 14 and divided the sum by 4, getting 17. (6 × x + 14) : 4 = 17 → 6 × x + 14 = 68 → 6 × x = 54 → x = 9.
Class activity
“Chain”: a chain of five equations where the root of one goes into the next. Teams race to solve the chain quickly and without mistakes.
Practice
1
Simplify and solve x + 25 = 9 × 6 − 17.
12
2
Solve y − 15 = 7 × 8 − 20.
51
3
Solve 560 : t = 8 × 7.
10
4
Solve z × 4 = 300 + 12 × 5.
90
5
We multiplied x by 6, added 14 and divided the sum by 4, getting 17. Find x.
9