First algebra and simple equations · Usually met around P5
Equations and setting them up
Name the unknown → find equal amounts → check.
How to do it
Method
Name the unknown → find equal amounts → check
3 books and $5 make $50: 3x + 5 = 50
Another way
Check by substituting
x = 15: 3 × 15 + 5 = 50
In full
An equation is an equality with an unknown (a letter) in it: 3x + 2 = 14 is an equation; 3x + 2 has no equals sign, so it isn't; 3 + 2 = 5 has no unknown, so it isn't either. To solve a word problem with an equation, first let a letter stand for the unknown, such as “each book costs x dollars”, then find two amounts in the problem that are equal and write them as an equality. You can follow the story's order (3x + 5 = 50) or think backwards first (3x = 50 − 5); both have the same solution. Then check: put the answer back into the problem and see that it fits.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Which of these is an equation?
- A. x + 17
- B. 4x + 17
- C. 4 + 17 = 21
- D. 4x + 17 = 57
Choose the right answer
Show the answer and working
Answer: D. 4x + 17 = 57
An equation is an equality with an unknown: it needs a letter and an equals sign.
Example 2
Ming had some stickers and buys 2 packs of 6, making 17 in all. With x for the stickers at first, the equation is x + 2 × 6 = 17. What is x?
Show the answer and working
Answer: 5
x = 17 − 2 × 6 = 5; check: 5 + 2 × 6 = 17.
Example 3
Which equation has the solution x = 5?
- A. 4x = 24
- B. x + 18 = 23
- C. x − 4 = 3
- D. 2x + 4 = 12
Choose the right answer
Show the answer and working
Answer: B. x + 18 = 23
Substitute x = 5 into each: only 5 + 18 = 23 holds.
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