Linear equations in one unknown · Ages 12–13
From words to an equation
One quantity, written two ways, with an equals sign between.
How to do it
Method
One quantity, written two ways, with an equals sign between
3 less than twice x is 11: 2x − 3 = 11
Another way
Choose the other as x
x + (x + 3) = 15 or x + (x − 3) = 15
In full
An equation writes one quantity in two ways. Choose x first (usually what the question asks for), then translate phrase by phrase: "3 more than x" is x + 3, "twice x" is 2x, "3 less than twice x" is 2x − 3. Then look for "altogether", "equals" or "the same" to place the equals sign. Or make a table: one row for each person or thing, what it was and what it became, and read the equation off. There is more than one right way: A has 3 more than B, 15 altogether. With B as x, x + (x + 3) = 15; with A as x, x + (x − 3) = 15. Both are right. Then try real numbers to see that the equation fits the story.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
5 bags, x sweets in each, 5 extra: 115 in all. The equation: x + = .
Fill in each blank
Show the answer and working
Answer: 5, 5, 115
5 bags hold 5x, plus 5, make 115: 5x + 5 = 115.
Example 2
Ka-yee has 2 times as much money as Ka-yan. Ka-yee spends $2 and Ka-yan is given $17, and then they have the same. With $x as Ka-yan's at first: Ka-yee now has $(x − 2), Ka-yan has $(x + ), and solving gives x = .
Fill in each blank
Show the answer and working
Answer: 2, 17, 19
Ka-yee had 2x, and after spending 2 has 2x − 2; Ka-yan with 17 more has x + 17. The same: 2x − 2 = x + 17, so x = 19.
Example 3
Tsz-hin has 6 more cards than May, 40 altogether. With x as Tsz-hin's, which equation is right?
- A. x + (x + 6) = 40
- B. x − (x − 6) = 40
- C. x + (x − 6) = 40
- D. 2x = 40
Choose the right answer
Show the answer and working
Answer: C. x + (x − 6) = 40
Tsz-hin has x, and May has 6 fewer, x − 6. Together 40: x + (x − 6) = 40.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1."6 added to 2 times x makes 50": which equation is it?
- A. 2(x + 6) = 50
- B. 2x + 6 = 50
- C. x + 2 + 6 = 50
- D. 6x + 2 = 50
Choose the right answer
Answer:
2."3 less than 9 times x is 58": which equation is it?
- A. 9x + 3 = 58
- B. 9(x − 3) = 58
- C. 3 − 9x = 58
- D. 9x − 3 = 58
Choose the right answer
Answer:
3.Ming buys 4 pens at $y each, pays $47 and gets $3 change. Which equation is right?
- A. 4y + 47 = 3
- B. 47 − 4y = 3
- C. 4y − 47 = 3
- D. 47 − y = 3
Choose the right answer
Answer:
4.Dad is 48 and the child x now. In 3 years, Dad will be 3 times the child's age. Which equation is right?
- A. 48 + 3 = 3x + 3
- B. 48 = 3(x + 3)
- C. 48 + 3 = 3(x + 3)
- D. 48 + 3 = 3x
Choose the right answer
Answer:
5.Ka-lok has 4 times as much money as Ka-yee. Ka-lok spends $39 and Ka-yee is given $15, and then they have the same. With $x as Ka-yee's at first: Ka-lok now has $(x − 39), Ka-yee has $(x + ), and solving gives x = .
Fill in each blank
Answer:
All the answers
- 1. B. 2x + 6 = 50
- 2. D. 9x − 3 = 58
- 3. B. 47 − 4y = 3
- 4. C. 48 + 3 = 3(x + 3)
- 5. 4, 15, 18
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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