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How many solutions can the equation |ax+b|=c have?

A) One solution
B) Two solutions
C) Zero solutions
D) Infinite solutions

User Kellogs
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1 Answer

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Final answer:

The equation |ax+b|=c can have zero, one, or two solutions depending on the values of a, b, and c. If c is negative, there are no solutions; if c is zero, there may be one solution; if c is positive, there can be two solutions.

Step-by-step explanation:

The equation |ax+b|=c can have different numbers of solutions depending on the values of a, b, and c. If c > 0, there are two potential solutions, since the absolute value expression can be equal to c or -c. However, if c = 0, there could be one solution where ax+b equals zero. In the case that c is less than zero, there are no real solutions because the absolute value is always non-negative. Therefore, the equation could have zero, one, or two solutions.

Considering the provided example where a = 1.00, b = 10.0, and c = -200, no real solutions exist because the absolute value can't be a negative number. In contrast, a quadratic equation of the form ax²+bx+c=0 can be solved using the quadratic formula and depending on the discriminant value (b²-4ac), might have two solutions, one solution, or no real solution.

User Vinita
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