From a situation to a line
A friend says: "Think of a number. Multiply by 3. Add 12. Divide by 3. Take your number away." The answer is 4. Why?
x. Multiply by 3: 3x.- Think of
x. Multiply by 3:3x. - Add 12:
3x + 12. - Divide by 3:
x + 4. - Take away
x:x + 4 − x = 4.
The last step takes away x. Only 12 ÷ 3 = 4 is left.
Rule: name the number x. Write each step as a line. Join like terms at the end.
Start at 7: 3 × 7 = 21, 21 + 12 = 33, 33 ÷ 3 = 11. Then 11 − 7 = 4. Start at 20: 60, 72, 24. And 24 − 20 = 4.
The same idea writes a bill as a line. Notebooks cost ₹18 each. Delivery is ₹25. For n notebooks the bill is 18n + 25. The 18 is the number in front of n. The 25 stands on its own. At n = 6 the bill is 108 + 25 = ₹133.
Watch out!
"5 less than a number" means take 5 from the number. That is n − 5, not 5 − n. At n = 12 the answer is 12 − 5 = 7, not −7.
Read the story. Slide the two numbers until the line fits.
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