fastest way to solve questions like how many solutions does this problem have?

JUWON

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Mar 30, 2017
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7
[FONT=KaTeX_Main]4[/FONT][FONT=KaTeX_Math]x[/FONT][FONT=KaTeX_Main]+[/FONT][FONT=KaTeX_Main]1[/FONT][FONT=KaTeX_Main]=[/FONT][FONT=KaTeX_Main]−[/FONT][FONT=KaTeX_Main]4[/FONT][FONT=KaTeX_Math]x[/FONT][FONT=KaTeX_Main]−[/FONT][FONT=KaTeX_Main]8

How many does this have?

A. No Solution
B. Exactly One Solution
C. Exactly Two Solutions
D. Infinitely many

How would I solve this step by step? When taking a time based test, is the best way just to solve directly. Or are there any tips/tricks I can use? [/FONT]
 
[FONT=KaTeX_Main]4[/FONT][FONT=KaTeX_Math]x[/FONT][FONT=KaTeX_Main]+[/FONT][FONT=KaTeX_Main]1[/FONT][FONT=KaTeX_Main]=[/FONT][FONT=KaTeX_Main]−[/FONT][FONT=KaTeX_Main]4[/FONT][FONT=KaTeX_Math]x[/FONT][FONT=KaTeX_Main]−[/FONT][FONT=KaTeX_Main]8

How many does this have?

A. No Solution
B. Exactly One Solution
C. Exactly Two Solutions
D. Infinitely many

How would I solve this step by step? When taking a time based test, is the best way just to solve directly. Or are there any tips/tricks I can use? [/FONT]
This is a linear equation → it cannot have "two solutions". To eliminate other possibilities, you would need to solve the equation.
 
[FONT=KaTeX_Main]4[/FONT][FONT=KaTeX_Math]x[/FONT][FONT=KaTeX_Main]+[/FONT][FONT=KaTeX_Main]1[/FONT][FONT=KaTeX_Main]=[/FONT][FONT=KaTeX_Main]−[/FONT][FONT=KaTeX_Main]4[/FONT][FONT=KaTeX_Math]x[/FONT][FONT=KaTeX_Main]−[/FONT][FONT=KaTeX_Main]8

How many does this have?

A. No Solution
B. Exactly One Solution
C. Exactly Two Solutions
D. Infinitely many

How would I solve this step by step? When taking a time based test, is the best way just to solve directly. Or are there any tips/tricks I can use? [/FONT]
As pointed out by denis, I managed to miss a minus sign so this post as originally written was not helpful and has effectively been deleted. Sorry about that.
 
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