Question 3 of 19intermediate✨ CreateShort Answer3 marks

Write 5 equations whose solution is x=−2x = -2.

Correct Answer

Five equations with solution x=−2x = -2 are: (1) x+2=0x + 2 = 0 (2) 2x=−42x = -4 (3) x+5=3x + 5 = 3 (4) 3x+6=03x + 6 = 0 (5) x+1=−1x + 1 = -1 Each of these equations gives x=−2x = -2 when solved.

Exercise: Figure it Out (Section 2) | Q: 1 | (Page Page 17)
For More Understanding

Explanation

The chapter discusses generating equations from a given solution. We can create equations by starting with x=−2x = -2 and performing operations on both sides, or by constructing expressions that evaluate correctly when x=−2x = -2. For example, starting with x=−2x = -2, adding 2 to both sides gives x+2=0x + 2 = 0. Multiplying both sides by 2 gives 2x=−42x = -4.

Solution Steps

  1. Start with the solution x=−2x = -2

  2. Add 2 to both sides: x+2=0x + 2 = 0

  3. Multiply both sides by 2: 2x=−42x = -4

  4. Add 5 to both sides then subtract 3: x+5=3x + 5 = 3

  5. Multiply by 3 and add 6: 3x+6=03x + 6 = 0

  6. Add 1 to both sides: x+1=−1x + 1 = -1

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