It is a function because all the inputs (x values) have one output (y value).
For something to be a function, inputs can only have ONE output, if an input has multiple outputs, it is not a function.
If different inputs have the same output, it is still a function because they don't have the same input value
Answer is True
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The short answer is that algebra doesn't work that way. You wouldn't divide *everything* by 2, but every term that contains a factor of 2.
In the expression
2 (6<em>x</em> - 1) + 2 (2<em>x</em> + 5)
both terms have a factor of 2 (the 2 out in front of them). They're the ones that get canceled when dividing by 2:
(2 (6<em>x</em> - 1) + 2 (2<em>x</em> + 5)) / 2 = 2/2 (6<em>x</em> - 1) + 2/2 (2<em>x</em> - 5)
… = 1 (6<em>x</em> - 1) + 1 (2<em>x</em> - 5)
… = (6<em>x</em> - 1) + (2<em>x</em> - 5)
and so on.
Looking ahead, it turns out that the equation is solved by <em>x</em> = 7. This makes 6<em>x</em> - 1 = 41 and 2<em>x</em> + 5 = 19. So the equation is saying that, if you make these replacements,
2×41 + 2×19 = 120
If you divide *everything* on the left by 2, you end up with fractions:
(2/2)×(41/2) + (2/2)×(19/2) = 41/2 + 19/2
but 41 + 19 = 60, so the end result would be 30, but that's not the same as 120/2 = 60.
Answer:
x<-3.5 or x<2
Step-by-step explanation:
2x²+3x<14
2x²+3x-14<0
2x²-4x+7x-14<0
2x(x-2)+7(x-2)<0
(2x+7)(x-2)<0
2x+7<0 or x-2<0
2x<-7 or x<2
x<-3.5
