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2 votes
Find the missing number/s so that the equation has One solution.

Select all that apply.



__x + 3 = –4x + 17

a
2
b
5
c
7
d
-4

User Clowwindy
by
7.3k points

1 Answer

1 vote

Answer: Choice A, Choice B, Choice C

In other words, it's nearly everything but choice D.

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Step-by-step explanation:

Let's say we select "2" as the thing to fill the blank.

2x+3 = -4x+17

2x+4x = 17-3

6x = 14

x = 14/6

x = 7/3

We get one solution in this case.

The same applies for the values 5 and 7. I'll let you do those steps.

In contrast, if we filled the blank with -4, then,

-4x+3 = -4x+17

-4x+4x = 17-3

0x = 14

0 = 14

We get a contradiction which leads to "no solutions".

Visually, the equations y = -4x+3 and y = -4x+17 are parallel lines that never intersect. We need them to intersect if we want a solution. Recall that parallel lines have equal slopes but different y-intercepts. Both sides have a slope of -4 in this case.

Therefore, the quick rule of thumb is this: if the slopes are not equal, then the linear equation has exactly one solution.

User Eudore
by
7.8k points
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