AlgebraVery hardConstant for infinitely many solutions
Algebra practice question
The equation 6x + 9 = 3(2x + b), where b is a constant, has infinitely many solutions. What is the value of b?
Answer: 3
Expand the right side: 6x + 3b. For 6x + 9 = 6x + 3b to hold for every x, the constants must match: 3b = 9, so b = 3.
Common wrong answers
- If you answered 0
- 0 would give 6x + 9 = 6x, which is never true.
- If you answered 6
- 6 is the coefficient of x, not b.
- If you answered 9
- 9 is 3b, one step short; the 3 outside the parentheses multiplies b.
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