Question

How many solutions does the equation below have. *The answer choices are below*

Answer 1

Answer:

The answer is one solution

Step-by-step explanation:

1)2(b+3)-17 = 3b-7+b

2)2b+6-17 = 4b-7

3)2b-11 = 4b-7

4)-11+7 = 4b-2b

5)-4 = 2b

6)2b = -4

7)b = -4/2

Final your answer is b = -2

Answer 2

Answer: D) One solution

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Work Shown:

2(b+3)-17 = 3b-7+b

2b+6-17 = 4b-7

2b-11 = 4b-7

-11+7 = 4b-2b

-4 = 2b

2b = -4

b = -4/2

b = -2

There is one solution and it is b = -2

A quick way to tell we have one solution is to note that both sides are a linear expression, and that the slopes of each linear expression are different values. If you had two lines with the same slope, then you'd have either parallel lines or coinciding lines (leading to no solutions and infinitely many solutions respectively). When you have two lines with two different slopes, then they are guaranteed to intersect only once. That intersection point is the solution.