Solve: |2x-1|< 11 express the solution in interval notation

(-5,6)

Step-by-step explanation:

Study the two possibilities for the expression inside the absolute value symbol: a) the expression 2x-1 is larger or equal zero, in which case its absolute value is the same as 2x-1, and b) the case of  2x-1 smaller than zero for which the absolute value is taken as the opposite (negative of this) value: -2x+1

Case a) can be then written without using the absolute value symbol as:

2x - 1 < 11  and solving for x (by adding 1 on both sides of the inequality) gives:

2x < 12  

Now to find the actual x-values that verify the inequality, we divide both sides by 2:

x < 6

Case b) can be written without using the absolute value symbol as:

- 2x + 1 < 11 so we add 2x to oth sides of the inequality:

1 < 11 + 2x  and now subtract 11 from both sides:

-10 < 2x

As we did before, we isolate x on one side by dividing by 2 on both sides of the inequality:

-5 < x

Now we find the interval on the number line that represents all those x values strictly larger than -5 and smaller than 6.

Such gives us:  -5 < x < 6  which can be written in interval notation as:

(-5, 6)

Case b)

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step-by-step explanation:

just copy and paste it.

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the circle graph is not a function.

step-by-step explanation:

the graph of the circle is not a function.

because for a graph to be a function, each value of x must give one value of y

in the circle, the values of x for -2< x< 2 each give 2 values of y.

hence this is not a function.