Answer: Infinitely many solutions
Any real number works for x
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Work Shown:
[tex]6 - 2x - 1 = 4x+5 - 6x\\\\-2x+6 - 1 = 4x - 6x+5\\\\-2x+5 = -2x+5[/tex]
We get the same identical expression on both sides. So plugging any number in for x leads to getting the same number on both sides.
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For instance, if x = 0,
[tex]-2x+5 = -2x+5\\\\-2(0)+5 = -2(0)+5\\\\5 = 5\\\\[/tex]
which is a true statement. The same happens when we plug x = 0 into the original equation
[tex]6 - 2x - 1 = 4x+5 - 6x\\\\6 - 2(0) - 1 = 4(0)+5 - 6(0)\\\\6 - 0 - 1 = 0+5 - 0\\\\5 = 5\\\\[/tex]
